On the path edge-connectivity of graphs

被引：0
|
作者：
Zhang, Shumin [1 ]
机构：
[1] Qinghai Normal Univ, Sch Comp Technol, Xining 810008, Qinghai, Peoples R China
来源：
ARS COMBINATORIA | 2017年 / 135卷
基金：
美国国家科学基金会;
关键词：
Edge-connectivity; Steiner tree; packing; path edge-connectivity; lexicographic product; LEXICOGRAPHIC PRODUCT GRAPHS; PACKING STEINER TREES; EXTREMAL GRAPHS; NETWORKS; COMMUNICATION; VERTICES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Dirac showed that in a (k - 1)-connected graph there is a path through each k vertices. The path k-connectivity pi(k)(G) of a graph G, which is a generalization of Dirac's notion, was introduced by Hager in 1986. Recently, Mao introduced the concept of path k-edge-connectivity omega(k)(G) of a graph G. Denote by G o H the lexicographic product of two graphs G and H. In this paper, we prove that omega(4)(G o H) >= omega(4)(G)[3 vertical bar V(H)vertical bar/5) I for any two graphs G and H. Moreover, the bound is sharp.
引用
收藏
页码：51 / 69
页数：19
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