3-Successive C-edge coloring of graphs
Authors :
U. Aswathy 1 and Charles Dominic 2 *
Author Address :
1,2 CHRIST (Department of Mathematics, CHRIST(Deemed to be University)), Bangalore-560029, Karnataka, India.
*Corresponding author.
Abstract :
The \textit{$3$-successive $c$-edge coloring number} $\overline{\psi}^{'}_{3s}(G)$ 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 \textit{$3$}-successive $c$-edge coloring number. Also, we attempt to find bounds of $\overline{\psi}^{'}_{3s}(G)$ 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
Keywords :
3-successive $c$-edge coloring, 3-successive $c$-edge coloring number, 3-successive $c$-edge achromatic sum, 3-consecutive edge coloring number, anti ramsey number.
DOI :
Article Info :
Received : March 14, 2020; Accepted : April 24, 2020.
