k-restricted edge connectivity in (p+1)-clique-free graphs

被引:4
|
作者
Wang, Shiying [1 ,2 ]
Zhang, Lei [1 ]
Lin, Shangwei [1 ]
机构
[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China
[2] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
基金
国家教育部博士点专项基金资助; 中国国家自然科学基金;
关键词
Interconnection network; Graph; Restricted edge connectivity; Clique; SUFFICIENT CONDITIONS; DIAMETER; 2; GIRTH;
D O I
10.1016/j.dam.2014.10.008
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let G be a graph with vertex set V(G) and edge set E(G). An edge subset S c E(G) is called a k-restricted edge cut if G - S is not connected and every component of G - S has at least k vertices. The k-restricted edge connectivity of a connected graph G, denoted by 4(G), is defined as the cardinality of a minimum k-restricted edge cut. Let [X, (X) over bar] denote the set of edges between a vertex set X subset of V (G) and its complement (X) over bar = V(G)\X. A vertex set X subset of V (G) is called a lambda(k)-fragment if [X, (X) over bar] is a minimum k-restricted edge cut of G. Let xi(k)(G) = min{vertical bar[X, (X) over bar]vertical bar : vertical bar X vertical bar = k, G[X] is connected}. In this work, we give a lower bound on the cardinality of lambda(k)-fragments of a graph G satisfying lambda(k)(G) < xi(k)(G) and containing no (p + 1)-cliques. As a consequence of this result, we show a sufficient condition for a graph G with lambda(k)(G) = xi(k)(G). (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码:255 / 259
页数:5
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