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Published in:
01-11-2023
Dominated coloring in product graphs
Published in: Journal of Combinatorial Optimization | Issue 4/2023
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Abstract
The dominated coloring (dom-coloring) of a graph G is a proper coloring such that each color class is dominated by at least one vertex. The dominated chromatic number (dom-chromatic number) of G is the minimum number of color classes among all dominated colorings of G, denoted by \(\chi _{\text {dom}}(G)\). In this paper, we study the dominated coloring of Cartesian product, direct product, lexicographic product and strong product of some graphs.