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On fault-tolerant partition dimension of graphs
Journal of Intelligent & Fuzzy Systems ( IF 1.7 ) Pub Date : 2020-10-24 , DOI: 10.3233/jifs-201390
Kamran Azhar 1 , Sohail Zafar 1 , Agha Kashif 1 , Zohaib Zahid 1
Affiliation  

Fault-tolerant resolving partition is natural extension of resolving partitions which have many applications in different areas of computer sciences for example sensor networking, intelligent systems, optimization and robot navigation. For a nontrivial connected graph G (V (G) , E (G)), the partition representation of vertex v with respect to an ordered partition Π = {Si : 1 ≤ i ≤ k} of V (G) is the k-vector r(v|Π)=(d(v,Si))i=1k , where, d (v, Si) = min {d (v, x) |x ∈ Si}, for i ∈ {1, 2, …, k}. A partition Π is said to be fault-tolerant partition resolving set of G if r (u|Π) and r (v|Π) differ by at least two places for all u ≠ v ∈ V (G). A fault-tolerant partition resolving set of minimum cardinality is called the fault-tolerant partition basis of G and its cardinality the fault-tolerant partition dimension of G denoted by P(G) . In this article, we will compute fault-tolerant partition dimension of families of tadpole and necklace graphs.

中文翻译:

关于图的容错分区维

容错解析分区是解析分区的自然扩展,解析分区在计算机科学的不同领域具有许多应用,例如传感器网络,智能系统,优化和机器人导航。对于非平凡的连通图G(V(G),E(G)),顶点v相对于V(G)的有序分区Si = {Si:1≤i≤k}的分区表示为k-向量r(v |Π)=(d(v,Si))i = 1k,其中,d(v,Si)= min {d(v,x)| x∈Si},对于i∈{1,2 ,…,k}。如果对于所有u≠v∈V(G),r(u |Π)和r(v |Π)至少相差两个位置,则分区被称为G的容错分区解析集。最小基数的容错分区解析集称为G的容错分区基础,其基数称为G的容错分区维,用P(G)表示。在这篇文章中,
更新日期:2020-10-30
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