Total edge irregularity strength of a categorical product of two paths

An edge irregular total k-labeling of a graph G = (V, E) is a labeling f : V boolean OR E -> {1, 2,..., k} such that the total edge-weights wt(xy) = f(x) + f(xy) + f(y) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determine the exact value of the total edge irregularity strength of the categorical product of two paths P-n and P-m. Our result adds further support to a recent conjecture of Ivanco and Jendrol.