Abstract
An edge irregular total k-labeling phi: 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(1)y(1) their weights phi(x) +phi(xy) +phi(y) and phi(x(1)) + phi(x(1)y(1)) +phi(y(1)) 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.
We have determined the exact value of the total edge irregularity strength of the categorical product of a cycle and a path.