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arXiv · 2011.12496

The Paired Domination Number of Cubic Graphs

Bin Sheng·Changhong Lu
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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 γpr(G), is the size of its smallest paired dominating set. Goddard and Henning conjectured that γpr(G) {\leq} 4n/7 holds for every graph G with δ(G) {\geq} 3, except the Petersen Graph. In this paper, we prove this conjecture for cubic graphs.

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Bin Sheng, Changhong Lu. 2020-11-25. The Paired Domination Number of Cubic Graphs. https://arxiv.org/abs/2011.12496

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