Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 Dominated chromatic number of some kinds of the generalized Helm graphs 843 856 14872 10.22049/cco.2024.29283.1924 EN F. Poryousefi Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran A. Erfanian Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran M. Nasiri Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran Journal Article 2023 12 20 Let $G$ be a simple graph. The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$. The current study is devoted to investigate the dominated chromatic number of Helm graphs and some  kinds of its the generalizations. https://comb-opt.azaruniv.ac.ir/article_14872_97756ae6a244eafa01c2007870935e69.pdf