Edge Coloring by Total Labelings of 4-regular Circulant Graphs.
Résumé
Edge-coloring total $k$-labeling of a connected graph $G$ is an assignment $f$ of non negative integers to the vertices and edges of $G$ such that two adjacent edges $e=uv$ and $e'=uv'$ of $G$ have different weights. The weight of an edge $uv$ is defined by : $$w(e=uv) = f(u)+f(v)+f(e),$$ In this paper, we study the chromatic number of the edge coloring by total labeling of $4$-regular circulant graphs $C_n(1,k)$.