A dominator coloring of a graph  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  is called the dominator chromatic number, denoted as  In this paper, we obtain the dominator chromatic number of the lexicographic product of a path with certain graphs.

dominator chromatic number, lexicographic product, path, triple star, complete graph.

Received: June 29, 2024; Revised: February 5, 2025; Accepted: February 25, 2025; Published: March 10, 2025

How to cite this article: S. Megala, N. Mohanapriya, R. Karthika and R. Kalaivani, Dominator chromatic number of lexicographic product of path with certain graphs, Advances and Applications in Discrete Mathematics 42(4) (2025), 363-380.https://doi.org/10.17654/0974165825023

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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