On Edge Irregular Total Labeling of Categorical Product of Two Cycles

Abstract

An edge irregular total k-labeling ?:V(G)?E(G)?{1,2,?,k} of a graph G=(V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x?y? their weights ?(x)+?(xy)+?(y) and ?(x?)+?(x?y?)+?(y?) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. In this paper, we determine the exact value of the total edge irregularity strength of the categorical product of two cycles C n and C m , for n,m?3.