3-Successive C-edge coloring of graphs

Abstract

The 3 -successive $c$-edge coloring number $\bar{\psi}_{3 s}^{\prime}(G)$ of a graph $G$ is the highest number of colors that can occur in a coloring of the edges of $G$ such that every path on three edges has at most two colors. In this paper, we obtain some exact values of 3-successive $c$-edge coloring number. Also, we attempt to find bounds of $\bar{\psi}_{3 s}^{\prime}(G)$ for different product of graphs which includes Cartesian, direct, strong, rooted and corona. The 3-successive $c$-edge achromatic sum is the maximum sum of colors among all the 3-successive $c$-edge coloring of $G$ with highest number of colors. We also determine the 3-successive $c$-edge achromatic sum for some classes of graphs.