On Mixed Domination in Generalized Petersen Graphs

12/03/2018

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by   M. Rajaati, et al.

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Given a graph G = (V, E), a set S ⊆ V ∪ 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 γ_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 ∈{1, 2}. Our method also provides a new upper bound for other Petersen graphs.