Abstract
The strong product G(1) boxed times G(2) of graphs G(1) and G(2) is the graph with V(G(1)) x V(G(2)) as the vertex set, and two distinct vertices (x(1), x(2)) and (y(1), y(2)) are adjacent whenever for each i is an element of {1, 2} either x(i) = y(i) or x(i)y(i) is an element of E(G(i)).
An edge irregular total k-labeling phi : V boolean OR E -> {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 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.
We have determined the exact value of the total edge irregularity strength of the strong product of two paths P-n and P-m.