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arXiv · 1812.00977

On Mixed Domination in Generalized Petersen Graphs

M. Rajaati·M. R. Hooshmandasl·M. Alambardar Meybodi·B. Davvaz
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Abstract

Given a graph $G = (V, E)$, a set $S \subseteq V \cup E$ of vertices and edges is called a mixed dominating set if every vertex and edge that is not included in $S$ happens to be adjacent or incident to a member of $S$. The mixed domination number $\gamma_{md}(G)$ of the graph is the size of the smallest mixed dominating set of $G$. We present an explicit method for constructing optimal mixed dominating sets in Petersen graphs $P(n, k)$ for $k \in \{1, 2\}$. Our method also provides a new upper bound for other Petersen graphs.

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M. Rajaati, M. R. Hooshmandasl, M. Alambardar Meybodi, B. Davvaz. 2018-12-03. On Mixed Domination in Generalized Petersen Graphs. https://arxiv.org/abs/1812.00977

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