Injective coloring of generalized Mycielskian of graphs

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Bhanupriya C.K.; Sunitha M.S.

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Journal Paper

Paper Information

Journal: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION Year:2025 | Volume:10 | Issue:2 Page(s): 463-482

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Information Journal Paper

Title

Injective coloring of generalized Mycielskian of graphs

Author(s)

Bhanupriya C.K. | Sunitha M.S. | Issue Writer Certificate

Keywords

injective coloring

injective chromatic number

generalized Mycielskian

Abstract

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.

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