Results on r-hued edge coloring of corona product of some graphs

Abstract

We investigate the concept of r-hued edge coloring in simple graphs, where each edge must be adjacent to at least $\min{r, \deg(e)}$ edges of distinct colors, with $\deg(e)$ representing the number of edges adjacent to a given edge $e$. The smallest number of colors required for such a coloring in a graph $G$ is termed the r-hued edge chromatic number, denoted by $\chi'_r(G)$. In this study, we determine the r-hued edge chromatic number for specific graph operations, particularly the corona product of path graphs and cycle graphs, under the condition $r = \max{\deg(e)}$.