当前位置: X-MOL 学术Discrete Appl. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Comparing Wiener complexity with eccentric complexity
Discrete Applied Mathematics ( IF 1.1 ) Pub Date : 2021-02-01 , DOI: 10.1016/j.dam.2020.11.020
Kexiang Xu , Aleksandar Ilić , Vesna Iršič , Sandi Klavžar , Huimin Li

The transmission of a vertex $v$ of a graph $G$ is the sum of distances from $v$ to all the other vertices in $G$. The Wiener complexity of $G$ is the number of different transmissions of its vertices. Similarly, the eccentric complexity of $G$ is defined as the number of different eccentricities of its vertices. In this paper these two complexities are compared. The complexities are first studied on Cartesian product graphs. Transmission indivisible graphs and arithmetic transmission graphs are introduced to demonstrate sharpness of upper and lower bounds on the Wiener complexity, respectively. It is shown that for almost all graphs the Wiener complexity is not smaller than the eccentric complexity. Several families of graphs in which the complexities are equal are constructed. Using the Cartesian product, it is also proved that the eccentric complexity can be arbitrarily larger than the Wiener complexity.

中文翻译:

比较维纳复杂度和偏心复杂度

图$G$ 的顶点$v$ 的传输是$v$ 到$G$ 中所有其他顶点的距离之和。$G$ 的维纳复杂度是其顶点的不同传输次数。类似地,$G$ 的偏心复杂度定义为其顶点不同偏心的数量。本文对这两种复杂性进行了比较。首先在笛卡尔积图上研究复杂性。引入传输不可分图和算术传输图来分别证明 Wiener 复杂度的上限和下限的锐度。结果表明,几乎所有图的维纳复杂度都不小于偏心复杂度。构建了几个复杂度相等的图族。使用笛卡尔积,
更新日期:2021-02-01
down
wechat
bug