Bounds on the connected domination number of a graph

被引：20
|
作者：
Desormeaux, Wyatt J. [1 ]
Haynes, Teresa W. [1 ,2 ]
Henning, Michael A. [1 ]
机构：
[1] Univ Johannesburg, Dept Math, ZA-2006 Auckland Pk, South Africa
[2] E Tennessee State Univ, Dept Math & Stat, Johnson City, TN 37614 USA
来源：
DISCRETE APPLIED MATHEMATICS | 2013年 / 161卷 / 18期
基金：
新加坡国家研究基金会;
关键词：
Connected domination; Girth; Domination;
D O I：
10.1016/j.dam.2013.06.023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A subset S of vertices in a graph G = (V, E) is a connected dominating set of G if every vertex of V\S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number gamma(c)(G) The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then gamma(c) (G) >= g(G) - 2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus-Gaddum type results. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：2925 / 2931
页数：7
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