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DOMINATOR CHROMATIC NUMBER OF LEXICOGRAPHIC PRODUCT OF PATH WITH CERTAIN GRAPHS
Keywords:
dominator chromatic number, lexicographic product, path, triple star, complete graphDOI:
https://doi.org/10.17654/0974165825023Abstract
A dominator coloring of a graph $\mathscr{G}$ is a proper coloring in which every vertex is adjacent to at least one vertex from each color class. The minimum number of colors required to achieve a dominator coloring of $\mathscr{G}$ is called the dominator chromatic number, denoted as $\chi_d(\mathscr{G})$. In this paper, we obtain the dominator chromatic number of the lexicographic product of a path with certain graphs.
Received: June 29, 2024
Revised: February 5, 2025
Accepted: February 25, 2025
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