On Edge Irregular Total Labeling of Categorical Product of Two Cycles

An edge irregular total k-labeling φ: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 φ(x)+φ(xy)+φ(y) and φ(x′)+φ(x′y′)+φ(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 Cn and Cm, for n,m≥3.