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On Mixed Domination in Generalized Petersen Graphs (1812.00977v1)
Published 3 Dec 2018 in cs.DM and math.CO
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.