Dominated coloring in product graphs

Minhui Li (), Shumin Zhang () and Chengfu Ye ()
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Minhui Li: Qinghai Normal University
Shumin Zhang: Qinghai Normal University
Chengfu Ye: Qinghai Normal University

Journal of Combinatorial Optimization, 2023, vol. 46, issue 4, No 2, 11 pages

Abstract: 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 $$\chi _{\text {dom}}(G)$$ χ dom ( G ) . In this paper, we study the dominated coloring of Cartesian product, direct product, lexicographic product and strong product of some graphs.

Keywords: Dominated coloring; Dominated chromatic number; Product graphs; 05C05; 05C12; 05C76 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01094-7

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