Abstract
An edge irregular total k-labeling phi:V(G)a(a)E(G)->{1,2,aEuro broken vertical bar,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 phi(x)+phi(xy)+phi(y) and phi(x')+phi(x'y')+phi(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,ma parts per thousand yen3.