Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 10 2 2025 06 01 Injective coloring of generalized Mycielskian of graphs 463 482 14671 10.22049/cco.2023.28389.1526 EN C.K. Bhanupriya Department of Mathematics, National Institute of Technology Calicut, Kozhikode, Kerala, India M.S. Sunitha Department of Mathematics, National Institute of Technology Calicut, Kozhikode, Kerala, India 0000-0002-0090-9252 Journal Article 2023 03 13 The injective chromatic number $\chi_i(G)$ of a graph $G$ is the smallest number of colors required to color the vertices of $G$ such that any two vertices with a common neighbor are assigned distinct colors. The Mycielskian or Mycielski graph $\mu(G)$ of a graph $G$, introduced by Jan Mycielski in 1955 has the property that, these graphs have large chromatic number with small clique number. The generalized Mycielskian $\mu_m(G),m>0$ (also known as cones over graphs) are the natural generalizations of the Mycielski graphs. In this paper, sharp bounds are obtained for the injective chromatic number of generalized Mycielskian of any graph $G$. Further, the injective chromatic number of generalized Mycielskian of some special classes of graphs such as paths, cycles, complete graphs, and complete bipartite graphs are obtained. https://comb-opt.azaruniv.ac.ir/article_14671_a10144be196191c3e516280a7279b18d.pdf