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  • A PPA parity theorem about trees in a bipartite graph
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-22
    Kathie Cameron; Jack Edmonds

    We prove a new PPA parity theorem: Given a bipartite graph G with bipartition (A,B) where B is a set of even-degree vertices, and given a tree T∗ of G containing all of A, such that any vertex of B in T∗ has degree 2 in T∗ and such that each vertex of A which is not a leaf of T∗ is met by an odd number of edges not in T∗, then there is an even number of trees of G containing all of A, with degree 0

    更新日期:2020-04-22
  • Cycle energy and its size dependence
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-22
    Ivan Gutman

    The concept of cycle energy (CE) was introduced in the chemical literature as early as in the 1970s. In this paper, three theorems are proven, showing the dependence of CE on the size of the corresponding cycle. Cycles of size 4r+2 and 2r+1 increase CE, whereas cycles of size 4r decrease CE. Some generalizations of these results are also offered.

    更新日期:2020-04-22
  • Matroid optimization problems with monotone monomials in the objective
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-21
    Anja Fischer; Frank Fischer; S. Thomas McCormick

    In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. We present

    更新日期:2020-04-21
  • On k-rainbow domination in regular graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-21
    Boštjan Kuzman

    The k-rainbow domination problem is studied for regular graphs. We prove that the k-rainbow domination number γrk(G) of a d-regular graph for d≤k≤2d is bounded below by kn∕2d, where n is the order of a graph. We determine necessary conditions for regular graphs to attain this bound and find several examples. As an application, we determine exact k-rainbow domination numbers for all cubic Cayley graphs

    更新日期:2020-04-21
  • Decomposing a graph into shortest paths with bounded eccentricity
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-21
    Etienne Birmelé; Fabien de Montgolfier; Léo Planche; Laurent Viennot

    We introduce the problem of hub-laminar decomposition which generalizes that of computing a shortest path with minimum eccentricity (MESP). Intuitively, it consists in decomposing a graph into several paths that collectively have small eccentricity and meet only at their extremities. We show that a graph having such a decomposition with long enough paths can be decomposed in polynomial time with bounds

    更新日期:2020-04-21
  • Spectral characterization of the complete graph removing a path
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-21
    Muhuo Liu; Haiying Shan; Xiaofeng Gu

    A graph G is said to be A−DS if every graph having the same adjacency spectrum is isomorphic to G. Let Kn∖Pk be the graph obtained from the complete graph Kn with n vertices by removing all edges of a path Pk with k vertices. It was shown by Doob and Haemers that Kn∖Pn is A−DS. In 2014, Cámara and Haemers conjectured that Kn∖Pk is A−DS for every 2≤k≤n, and they succeeded in proving it for 2≤k≤6. Recently

    更新日期:2020-04-21
  • The preclusion numbers and edge preclusion numbers in a class of Cayley graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-20
    Guozhen Zhang

    Let G be a hierarchical network (graph) with vertex set V(G) and edge set E(G). The preclusion set of the subnetwork G′ (defined as a smaller network but with the same topological properties as the original one) in G is a subset V′ of V(G) such that G−V′ has no any subnetwork isomorphic to G′. The preclusion number of G′ in G is F(G′)=min{|V′|:V′ is the preclusion set of G′}. Similarly, the edge preclusion

    更新日期:2020-04-20
  • Spanning 2-forests and resistance distance in 2-connected graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-20
    Wayne Barrett; Emily J. Evans; Amanda E. Francis; Mark Kempton; John Sinkovic

    A spanning 2-forest separating vertices u and v of an undirected connected graph is a spanning forest with 2 components such that u and v are in distinct components. Aside from their combinatorial significance, spanning 2-forests have an important application to the calculation of resistance distance or effective resistance. The resistance distance between vertices u and v in a graph representing an

    更新日期:2020-04-20
  • The generalized matcher game
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-19
    Anna Bachstein; Wayne Goddard; Connor Lehmacher

    Recently the matcher game was introduced. In this game, two players create a maximal matching by one player repeatedly choosing a vertex and the other player choosing a K2 containing that vertex. One player tries to minimize the result and the other to maximize the result. In this paper we propose a generalization of this game where K2 is replaced by a general graph F. We focus here on the case of

    更新日期:2020-04-19
  • Structure connectivity and substructure connectivity of star graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-18
    Chunfang Li; Shangwei Lin; Shengjia Li

    The connectivity is an important measurement for the fault-tolerance of networks. The structure connectivity and substructure connectivity are two generalizations of the classical connectivity. For a fixed graph H, a set F of subgraphs of G is called an H-structure cut (resp., H-substructure cut) of G, if G−∪F∈FV(F) is disconnected and every element of F is isomorphic to H (resp., a connected subgraph

    更新日期:2020-04-18
  • The asymptotic value of graph energy for random graphs with degree-based weights
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-18
    Xueliang Li; Yiyang Li; Jiarong Song

    In this paper, we investigate the energy of a weighted random graph Gp(f) in Gn,p(f), in which each edge ij takes the weight f(di,dj), where dv is a random variable, the degree of vertex v in the random graph Gp of the Erdös–Rényi random graph model Gn,p, and f is a symmetric real function on two variables. Suppose |f(di,dj)|≤Cnm for some constants C,m>0, and f((1+o(1))np,(1+o(1))np)=(1+o(1))f(np,np)

    更新日期:2020-04-18
  • On highly palindromic words: The ternary case
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-18
    Kristina Ago; Bojan Bašić

    A word over an n-ary alphabet is called minimal-palindromic if it does not contain palindromic subwords whose length is greater than ⌈|w|n⌉ (note that each n-ary word must contain a palindromic subword of at least that length: for example, a subword consisting of a prevalent letter, which explains the term “minimal-palindromic”). The MP-ratio of a given word w is defined as the quotient |rws||w|, where

    更新日期:2020-04-18
  • The Schrijver system of the flow cone in series–parallel graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-17
    Michele Barbato; Roland Grappe; Mathieu Lacroix; Emiliano Lancini; Roberto Wolfler Calvo

    We represent a flow of a graph G=(V,E) as a couple (C,e) with C a circuit of G and e an edge of C, and its incidence vector is the 0∕±1 vector χC∖e−χe. The flow cone of G is the cone generated by the flows of G and the unit vectors. When G has no K5-minor, this cone can be described by the system x(M)≥0 for all multicuts M of G. We prove that this system is box-totally dual integral if and only if

    更新日期:2020-04-17
  • Characterizations, probe and sandwich problems on (k,ℓ)-cographs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-17
    Fernanda Couto; Luerbio Faria; Sylvain Gravier; Sulamita Klein; Vinicius F. dos Santos

    A cograph is a graph without an induced 3-edge path. A graph is (k,ℓ) if its vertex set can be partitioned into at most k independent sets and ℓ cliques. (k,ℓ)-cographs already have a forbidden induced subgraphs characterization, but no structural characterization is known, except for (1,1)-cographs, i.e. threshold graphs. In this paper, we present a structural characterization and a decomposition

    更新日期:2020-04-17
  • On coloring the arcs of biregular graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-17
    Italo J. Dejter

    Recalling each edge of a graph H has 2 oppositely oriented arcs, each vertex v of H is identified with the set of arcs, denoted (v,e), departing from v along the edges e of H incident to v. Let H be a (λ,μ)-biregular graph with bipartition (Y,X), where |Y|=kμ and |X|=kλ, (0

    更新日期:2020-04-17
  • Burning number of caterpillars
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-16
    Huiqing Liu; Xuejiao Hu; Xiaolan Hu

    Graph burning is a deterministic discrete time graph process that can be interpreted as a model for the spread of influence in social networks. The burning number b(G) of a graph G is the minimum number of steps in a graph burning process for G. Bonato et al. (2014) conjectured that b(G)≤⌈n⌉ for any connected graph G of order n. In this paper, we confirm this conjecture for caterpillars. We also determine

    更新日期:2020-04-16
  • Power domination in regular claw-free graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-14
    Changhong Lu; Rui Mao; Bing Wang

    In this paper, we show that the power domination number of a connected 4-regular claw-free graph on n vertices is at most n+15, and the bound is sharp. The statement disproves the conjecture presented by Dorbec et al. (2013).

    更新日期:2020-04-14
  • On the extremal values of the eccentric distance sum of trees with a given maximum degree
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-14
    Lianying Miao; Jingru Pang; Shoujun Xu

    Let G be a simple connected graph. The eccentric distance sum (EDS) of G is defined as ξd(G)=∑v∈VεG(v)DG(v), where εG(v) is the eccentricity of the vertex v and DG(v)=∑u∈VdG(u,v) is the sum of all distances from the vertex v. In this paper, the extremal tree which minimizes the EDS among n-vertex trees of given maximum degree is characterized. This proves Conjecture 3.2 posed in Miao et al., (2015)

    更新日期:2020-04-14
  • On energy and Laplacian energy of chain graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-11
    Kinkar Chandra Das; Abdullah Alazemi; Milica Anđelić

    Let G be a simple graph of order n. The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. The Laplacian energy of the graph G is defined as LE=LE(G)=∑i=1nμi−d¯,where μ1,μ2,…,μn−1,μn=0 are the Laplacian eigenvalues, and d¯ is the average degree of graph G. In this paper we present some lower and upper bounds on E(G) of chain graph G. From this

    更新日期:2020-04-11
  • The target location function on finite trees
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-11
    Trevor Leach; F.R. McMorris; Henry Martyn Mulder; R.C. Powers

    A location function on a finite connected graph G takes as input any k-tuple of vertices (a profile) and outputs a single vertex. If G is a full y gated graph, then a target location function is defined by a predetermined vertex (the target) and outputs the unique vertex belonging to the convex closure of the profile which is closest to the target. If G is a finite tree, then any target function on

    更新日期:2020-04-11
  • Non-hamiltonian 1-tough triangulations with disjoint separating triangles
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-11
    Jun Fujisawa; Carol T. Zamfirescu

    In this note, we consider triangulations of the plane. Ozeki and the second author asked whether there are non-hamiltonian 1-tough triangulations in which every two separating triangles are disjoint. We answer this question in the affirmative and strengthen a result of Nishizeki by proving that there are infinitely many non-hamiltonian 1-tough triangulations with pairwise disjoint separating triangles

    更新日期:2020-04-11
  • On the edge-Szeged index of unicyclic graphs with perfect matchings
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-11
    Shengjie He; Rong-Xia Hao; Yan-Quan Feng

    The edge-Szeged index of a graph G is defined as Sze(G)=∑uv∈E(G)mu(uv|G)mv(uv|G), where mu(uv|G) (resp., mv(uv|G)) is the number of edges whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), respectively. In this paper, we characterize the graphs with minimum edge-Szeged index among all the unicyclic graphs with given order and perfect matchings.

    更新日期:2020-04-11
  • The harmonic index of a graph and its DP-chromatic number
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-10
    Jian-Bo Lv; Jianxi Li

    The harmonic index H(G) of a graph G is defined as the sum of the weights 2d(u)+d(v) of all edges uv of G, where d(u) is the degree of the vertex u in G. The DP-chromatic number of G, denoted by χDP(G), is the minimum number k such that G is DP-k-colorable. In this paper, we show that χDP(G)≤2H(G), and the equality holds if and only if G is a complete graph possibly with some additional isolated vertices

    更新日期:2020-04-10
  • A 34-approximation of Vizing’s conjecture for claw-free graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-10
    Boštjan Brešar; Michael A. Henning

    Vizing’s conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. We prove that for any claw-free graph G and an arbitrary graph H, the inequality γ(G□H)≥34γ(G)γ(H) always holds.

    更新日期:2020-04-10
  • Restricted matching in plane triangulations and near triangulations
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-10
    R.E.L. Aldred; Michael D. Plummer; Watcharintorn Ruksasakchai

    We present a complete description of matching extendability in 5-connected planar triangulations after the deletion of a set of vertices of appropriate parity. We also introduce a variation of distance restricted matching extension in the setting of vertex deleted graphs and prove some results which generalize certain previous results obtained for 5-connected planar triangulations.

    更新日期:2020-04-10
  • General eccentric connectivity index of trees and unicyclic graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-10
    Tomáš Vetrík; Mesfin Masre

    We introduce the general eccentric connectivity index of a graph G, ECIα(G)=∑v∈V(G)eccG(v)dGα(v) for α∈R, where V(G) is the vertex set of G, eccG(v) is the eccentricity of a vertex v and dG(v) is the degree of v in G. We present lower and upper bounds on the general eccentric connectivity index for trees of given order, trees of given order and diameter, and trees of given order and number of pendant

    更新日期:2020-04-10
  • Graphs with the second and third maximum Wiener indices over the 2-vertex connected graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-10
    Stéphane Bessy; François Dross; Martin Knor; Riste Škrekovski

    Wiener index, defined as the sum of distances between all unordered pairs of vertices, is one of the most popular molecular descriptors. It is well known that among 2-vertex connected graphs on n≥3 vertices, the cycle Cn attains the maximum value of Wiener index. We show that the second maximum graph is obtained from Cn by introducing a new edge that connects two vertices at distance two on the cycle

    更新日期:2020-04-10
  • Enumeration and extensions of word-representants
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-10
    Marisa Gaetz; Caleb Ji

    Given a finite word w over a finite alphabet V, consider the graph with vertex set V and with an edge between two elements of V if and only if the two elements alternate in the word w. Such a graph is said to be word-representable or 11-representable by the word w; this latter terminology arises from the phenomenon that the condition of two elements x and y alternating in a word w is the same as the

    更新日期:2020-04-10
  • On matroid parity and matching polytopes
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-10
    Konstantinos Kaparis; Adam N. Letchford; Ioannis Mourtos

    The matroid parity (MP) problem is a powerful (and NP-hard) extension of the matching problem. Whereas matching polytopes are well understood, little is known about MP polytopes. We prove that, when the matroid is laminar, the MP polytope is affinely congruent to a perfect b-matching polytope. From this we deduce that, even when the matroid is not laminar, every Chvátal–Gomory cut for the MP polytope

    更新日期:2020-04-10
  • Structurally parameterized d-scattered set
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-09
    Ioannis Katsikarelis; Michael Lampis; Vangelis Th. Paschos

    In d-Scattered Set we are given an (edge-weighted) graph and are asked to select at least k vertices, so that the distance between any pair is at least d, thus generalizing Independent Set. We provide upper and lower bounds on the complexity of this problem with respect to various standard graph parameters. In particular, we show the following: • For any d≥2, an O∗(dtw)-time algorithm, where tw is

    更新日期:2020-04-09
  • Algorithmic enumeration of surrounding polygons
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-09
    Katsuhisa Yamanaka; David Avis; Takashi Horiyama; Yoshio Okamoto; Ryuhei Uehara; Tanami Yamauchi

    We are given a set S of points in the Euclidean plane. We assume that S is in general position. A simple polygon P is a surrounding polygon of S if each vertex of P is a point in S and every point in S is either inside P or a vertex of P. In this paper, we present an enumeration algorithm of the surrounding polygons for a given point set. Our algorithm is based on reverse search by Avis and Fukuda

    更新日期:2020-04-09
  • Compact cactus representations of all non-trivial min-cuts
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-08
    On-Hei S. Lo; Jens M. Schmidt; Mikkel Thorup

    Recently, Kawarabayashi and Thorup presented the first deterministic edge-connectivity recognition algorithm in near-linear time. A crucial step in their algorithm uses the existence of vertex subsets of a simple graph G on n vertices whose contractions leave a multigraph with Õ(n∕δ) vertices and Õ(n) edges that preserves all non-trivial min-cuts of G, where δ is the minimum degree of G and Õ hides

    更新日期:2020-04-08
  • Constructive characterizations concerning weak Roman domination in trees
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-08
    Abel Cabrera-Martínez; Ismael G. Yero

    Given a graph G, we consider γr(G), γ{R2}(G), γr2(G) and γR(G) as the weak Roman domination number, the Roman {2}-domination number, the 2-rainbow domination number and the Roman domination number of G, respectively. It is known that γr(G)≤γ{R2}(G)≤γr2(G)≤γR(G) holds for any graph G. In connection with this, constructive characterizations of the trees T that satisfy the equalities above that are related

    更新日期:2020-04-08
  • Complexity of planar signed graph homomorphisms to cycles
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-08
    François Dross; Florent Foucaud; Valia Mitsou; Pascal Ochem; Théo Pierron

    We study homomorphism problems of signed graphs from a computational point of view. A signed graph is an undirected graph where each edge is given a sign, positive or negative. An important concept when studying signed graphs is the operation of switching at a vertex, which is to change the sign of each incident edge. A homomorphism of a graph is a vertex-mapping that preserves the adjacencies; in

    更新日期:2020-04-08
  • Double domination in lexicographic product graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-07
    Abel Cabrera Martínez; Suitberto Cabrera García; J.A. Rodríguez-Velázquez

    In a graph G, a vertex dominates itself and its neighbours. A subset S⊆V(G) is said to be a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality among all double dominating sets of G is the double domination number. In this article, we obtain tight bounds and closed formulas for the double domination number of lexicographic product graphs G∘H in terms

    更新日期:2020-04-07
  • Vertex alternating-pancyclism in 2-edge-colored generalized sums of graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-07
    Narda Cordero-Michel; Hortensia Galeana-Sánchez

    An alternating cycle in a 2-edge-colored graph is a cycle such that any two consecutive edges have different colors. Let G1, …, Gk be a collection of pairwise vertex disjoint 2-edge-colored graphs. The colored generalized sum of G1, …, Gk, denoted by ⊕i=1kGi, is the set of all 2-edge-colored graphs G such that: (i) V(G)=⋃i=1kV(Gi), (ii) G〈V(Gi)〉≅Gi for i=1,…,k as edge-colored graphs where G〈V(Gi)〉

    更新日期:2020-04-07
  • On the number of almost envy-free allocations
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-07
    Warut Suksompong

    Envy-freeness is a standard benchmark of fairness in resource allocation. Since it cannot always be satisfied when the resource consists of indivisible items even when there are two agents, the relaxations envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) are often considered. We establish tight lower bounds on the number of allocations satisfying each of these benchmarks in

    更新日期:2020-04-07
  • Edge decomposition of connected claw-free cubic graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-06
    Yanmei Hong; Qinghai Liu; Nannan Yu

    It was conjectured by Hoffmann–Ostenhof that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a family of disjoint cycles. In this paper, we show that the conjecture is true for connected claw-free cubic graphs, and, furthermore, any edge not contained any triangle appears only on the tree or on the matching. Then we show that the edge set of every

    更新日期:2020-04-06
  • Cube-free resonance graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-06
    Zhongyuan Che

    Let G be a plane elementary bipartite graph with more than two vertices. Then its resonance graph Z(G) is a median graph and the set M(G) of all perfect matchings of G with a specific partial order is a finite distributive lattice. In this paper, we prove that Z(G) is cube-free if and only if it can be obtained from an edge by a sequence of convex path expansions with respect to a reducible face decomposition

    更新日期:2020-04-06
  • Some notes on the extremal k-generalized quasi-unicyclic graphs with respect to Zagreb indices
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-04
    Muhuo Liu; Kun Cheng; Ioan Tomescu

    In this note, we point out some problems in the proofs and the main results of Javaid, Jamil and Tomescu (2019), and we also give the correct versions of them.

    更新日期:2020-04-04
  • Edge-colouring graphs with bounded local degree sums
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-04
    L.M. Zatesko; A. Zorzi; R. Carmo; A.L.P. Guedes

    Deciding if a general graph G with maximum degree Δ is Class 1 (Δ-edge-colourable) is an NP-complete problem. Therefore, for over 30 years there has been much work aimed at identifying graph classes wherein Δ-edge-colourability is equivalent to non-subgraph-overfullness, a polynomial-time decidable property. A graph G is said to be subgraph-overfull (SO) if it has a subgraph H with the same maximum

    更新日期:2020-04-04
  • Finding dominating induced matchings in S1,1,5-free graphs in polynomial time
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-03
    Andreas Brandstädt; Raffaele Mosca

    Let G=(V,E) be a finite undirected graph. An edge set E′⊆E is a dominating induced matching (d.i.m.) in G if every edge in E is intersected by exactly one edge of E′. The Dominating Induced Matching (DIM) problem asks for the existence of a d.i.m. in G; this problem is also known as the Efficient Edge Domination problem; it is the Efficient Domination problem for line graphs. The DIM problem is NP-complete

    更新日期:2020-04-03
  • Adynamic coloring of graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-03
    Mária Šurimová; Borut Lužar; Tomáš Madaras

    For a graph G with at least one vertex with independent neighborhood, an adynamic coloring of G is a proper vertex coloring of G such that there exists at least one vertex of degree at least 2 whose all neighbors have the same color. We explore basic properties of adynamic colorings and their relations to proper and dynamic colorings. We also establish a number of results for planar graphs; in particular

    更新日期:2020-04-03
  • Multilevel secret sharing schemes arising from the normal rational curve
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-04-02
    Stefania Caputo; Gábor Korchmáros; Angelo Sonnino

    Multilevel secret sharing schemes are used in cryptography when a responsibility has to be delegated to qualified groups of participants rather than to a single one. In the present paper we propose a mathematical model for such a scheme based on projective geometry over a finite field. The main ingredients are normal rational curves and their osculating subspaces.

    更新日期:2020-04-02
  • Normalized Laplacian spectrum of complete multipartite graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-30
    Shaowei Sun; Kinkar Chandra Das

    The spectrum of the normalized Laplacian matrix of a graph provides many structural information of the graph, and it has many applications in numerous areas and in different guises. Let G be a complete k-partite graph with k≥3. In this paper, we give the necessary and sufficient condition for G which is determined by their normalized Laplacian spectrum. Moreover, we obtain a majorization theory of

    更新日期:2020-03-30
  • Toughness and prism-hamiltonicity of P4-free graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-28
    M.N. Ellingham; Pouria Salehi Nowbandegani; Songling Shan

    The prism over a graph G is the product G□K2, i.e., the graph obtained by taking two copies of G and adding a perfect matching joining the two copies of each vertex by an edge. The graph G is called prism-hamiltonian if it has a hamiltonian prism. Jung showed that every 1-tough P4-free graph with at least three vertices is hamiltonian. In this paper, we extend this to observe that for k≥1 a P4-free

    更新日期:2020-03-28
  • Maximum nullity and zero forcing number on graphs with maximum degree at most three
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-28
    Meysam Alishahi; Elahe Rezaei-Sani; Elahe Sharifi

    A dynamic coloring of a graph G starts with an initial subset F⊆V(G) of colored vertices, while all the remaining vertices are non-colored. At each time step, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set F is called a zero forcing set of G if, by iteratively applying the forcing process, every vertex in G becomes colored. The

    更新日期:2020-03-28
  • Stack words and a bound for 3-stack sortable permutations
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-27
    Miklós Bóna

    We use stack words to find a new, simple proof for the best known upper bound for the number of 3-stack sortable permutations of a given length. This is the first time that stack words are used to obtain such a result.

    更新日期:2020-03-27
  • Independent (k+1)-domination in k-trees
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-24
    Mieczysław Borowiecki; Anna Fiedorowicz; Elżbieta Sidorowicz; Zsolt Tuza

    The problem of independent k-domination is defined as follows: A subset S of the set of vertices of a graph G is called independent k-dominating in G, if S is both independent and k-dominating. In 2003, Haynes, Hedetniemi, Henning and Slater studied this problem in the class of trees, and gave the characterization of all trees having an independent 2-dominating set. They also proved that if such a

    更新日期:2020-03-24
  • On the degree Kirchhoff index of unicyclic graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-24
    Xuli Qi; Bo Zhou

    Let G be a connected graph with vertex set V(G). The degree Kirchhoff index of G is defined as Kf∗(G)=∑{u,v}⊆V(G)dG(u)dG(v)RG(u,v), where dG(u) denotes the degree of the vertex u in G, and RG(u,v) denotes the resistance distance between vertices u and v in G. In this paper, we determine maximum degree Kirchhoff index of n-vertex unicyclic graphs with fixed maximum degree, the first seven maximum degree

    更新日期:2020-03-24
  • Efficient design methods of low-weight correlation-immune functions and revisiting their basic characterization
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-23
    S. Kudin; E. Pasalic

    Correlation immunity (CI) of Boolean functions is an important concept relevant both in the design of nonlinear combiners and for the protection against side-channel cryptanalysis to name a few applications. In this article we give further simplification of the proofs of some known characterizations of these functions, including some new results related to certain properties of the algebraic normal

    更新日期:2020-03-23
  • Strong chromatic index of K1,t-free graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-21
    Michał Dębski; Konstanty Junosza-Szaniawski; Małgorzata Śleszyńska-Nowak

    A strong edge-coloring of a graph G is a coloring of the edges of G such that each color class is an induced matching. The strong chromatic index of G is the minimum number of colors in a strong edge-coloring of G. We show that the strong chromatic index of a claw-free graph with maximum degree Δ is at most 1.125Δ2+Δ, which confirms the conjecture of Erdős and Nešetřil from 1985 for this class of graphs

    更新日期:2020-03-21
  • On the equivalence of cylinder tilings and planar electric networks
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-20
    Ben Amiet; Greg Markowsky; José Palacios

    In the famous paper (Brooks et al., 1940) an equivalence was established between planar electric networks and tilings of cylinders. However, the proof given there is rather difficult and requires knowledge of a larger theory. We give a simple new proof of this equivalence. Furthermore, there is a well known relationship between electric networks and random walks. We show how the tiling associated with

    更新日期:2020-03-20
  • On the structure of 4-regular planar well-covered graphs
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-20
    Arthur S. Finbow; Bert L. Hartnell; Michael D. Plummer

    A graph G is said to be well-covered if every maximal independent set of vertices has the same cardinality. It is unknown whether membership in this class of graphs is polynomially decidable. In this paper we focus on the study of well-covered graphs which are 4-regular and planar.

    更新日期:2020-03-20
  • Packing, partitioning, and covering symresacks
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-20
    Christopher Hojny

    In this paper, we consider symmetric binary programs that contain set packing, partitioning, or covering inequalities. To handle symmetries as well as set packing, partitioning, or covering constraints simultaneously, we introduce constrained symresacks which are the convex hulls of all binary points that are lexicographically not smaller than their image w.r.t. a coordinate permutation and which fulfill

    更新日期:2020-03-20
  • Perfect double Roman domination of trees
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-20
    Ayotunde T. Egunjobi; Teresa W. Haynes

    For a graph G with vertex set V(G) and function f:V(G)→{0,1,2,3}, let Vi be the set of vertices assigned i by f. A perfect double Roman dominating function of a graph G is a function f:V(G)→{0,1,2,3} satisfying the conditions that (i) if u∈V0, then u is either adjacent to exactly two vertices in V2 and no vertex in V3 or adjacent to exactly one vertex in V3 and no vertex in V2; and (ii) if u∈V1, then

    更新日期:2020-03-20
  • 1-2-3 Conjecture in digraphs: More results and directions
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-20
    Julien Bensmail; Kasper Lyngsie

    Horňak, Przybyło and Woźniak recently proved that, a small class of obvious exceptions apart, every digraph can be 4-arc-weighted so that, for every arc uv⃗, the sum of weights incoming to u is different from the sum of weights outgoing from v. They conjectured a stronger result, namely that the same statement with 3 instead of 4 should also be true. We verify this conjecture in this work. This work

    更新日期:2020-03-20
  • Signed analogue of general Kotzig–Lovász decomposition
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-20
    Nanao Kita

    This paper is the first from a series of papers that establish a common analogue of the strong component and basilica decompositions for bidirected graphs. A bidirected graph is a graph in which a sign + or − is assigned to each end of each edge, and therefore is a common generalization of digraphs and signed graphs. Unlike digraphs, the reachabilities between vertices by directed trails and paths

    更新日期:2020-03-20
  • How to build a graph in n days: Some variations of graph assembly
    Discrete Appl. Math. (IF 1.041) Pub Date : 2020-03-20
    Aria L. Dougherty; Nicholas Mayers; Robert Short

    In a recent article by Bona and Vince, the authors studied the concept of an assembly tree for a graph motivated by the way that macromolecules assemble. Assembly trees act as record keeping devices for the construction of a given graph from its vertices. In the original article, graphs were to be assembled following an edge gluing rule for the vertices. In this paper, we first define and enumerate

    更新日期:2020-03-20
  • Sparse obstructions for minor-covering parameters
    Discrete Appl. Math. (IF 1.041) Pub Date : 2019-11-01
    Dimitris Chatzidimitriou; Dimitrios M. Thilikos; Dimitris Zoros

    Given a finite set of graphs H and a non-negative integer k, we define Ak(H) as the set containing every graph G that has k vertices whose removal provides a graph without any of the graphs in H as a minor. It is known that if H contains at least one planar graph then each obstruction in Ak(H) has at most kcH vertices, for some cH depending only on the choice of H. In this paper, we investigate the

    更新日期:2019-11-01
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