On Mixed Domination in Generalized Petersen Graphs
Abstract
Given a graph G = (V, E), a set S ⊂eq 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 γmd(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.
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