Edge coloring total k-labeling of generalized Petersen graphs

• We study the edge coloring total k-labeling.
• We consider generalized Petersen graphs.
• We compute the exact value for the chromatic number.
• We give the coloring algorithms.

The 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 uv   and uv′uv′ of G have different weights. The weight of an edge uv   is defined by: w(uv)=f(u)+f(v)+f(uv)w(uv)=f(u)+f(v)+f(uv). In this paper, we study the chromatic number of the edge coloring total k-labeling of generalized Petersen graphs and we propose exact values.