Edge Coloring by Total Labelings of 4-regular Circulant Graphs

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=uve=uv and e′=uv′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).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 Cn(1,k)Cn(1,k).