Effects of Some Operations on Domination Chromatic Number in Graphs
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For a simple graph G, a domination coloring of G is a proper vertex coloring such that every vertex of G dominates at least one color class, and every color class is dominated by at least one vertex. The domination chromatic number, denoted by χ_dd(G), is minimum number of colors among all domination colorings of G. In this paper, we discuss the effects of some typical operations on χ_dd(G), such as vertex (edge) removal, vertex (edge) contraction, edge subdivision, and cycle extending.
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