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 = u v and e ′ = u v ′ of G have different weights. The weight of an edge uv is defined by: w ( e = u v ) = 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 ) .