The Paired Domination Number of Cubic Graphs
Combinatorics
2020-11-26 v1
Abstract
Let G be a simple undirected graph with no isolated vertex. A paired dominating set of G is a dominating set which induces a subgraph that has a perfect matching. The paired domination number of G, denoted by {\gamma}pr(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that {\gamma}pr(G) {\leq} 4n/7 holds for every graph G with {\delta}(G) {\geq} 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.
Cite
@article{arxiv.2011.12496,
title = {The Paired Domination Number of Cubic Graphs},
author = {Bin Sheng and Changhong Lu},
journal= {arXiv preprint arXiv:2011.12496},
year = {2020}
}