Elsevier

Discrete Mathematics

Volume 309, Issue 5, 28 March 2009, Pages 1142-1162
Discrete Mathematics

An upper bound on the domination number of n-vertex connected cubic graphs

https://doi.org/10.1016/j.disc.2007.12.009Get rights and content
Under an Elsevier user license
open archive

Abstract

In 1996, Reed proved that the domination number γ(G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. This bound is sharp for cubic graphs if there is no restriction on connectivity. In this paper we show that γ(G)4n/11 for every n-vertex cubic connected graph G if n>8. Note that Reed’s conjecture that γ(G)n/3 for every connected cubic n-vertex graph G is not true.

Keywords

Cubic graphs
Domination
Connected graphs

Cited by (0)