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.
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Funding
This work is supported by the Science Found of Qinghai Province (No.2021-ZJ-703), the National Science Foundation of China (Nos.11661068, 12261074 and 12201335)
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Li, M., Zhang, S. & Ye, C. Dominated coloring in product graphs. J Comb Optim 46, 24 (2023). https://doi.org/10.1007/s10878-023-01094-7
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DOI: https://doi.org/10.1007/s10878-023-01094-7