Abstract
As an edge variant of the well-known irregularity strength of a graph G = (V, E) we investigate edge irregular total k-labeling phi: V boolean OR E -> {1, 2,..., k} such that phi(u) + phi(uv) + phi(v) not equal phi(u') + phi(u'v') + phi(v') for every pair of different edges uv, u'v' is an element of E. The smallest possible k is the total edge irregularity strength of G. We determine the exact value of the total edge irregularity strength of the strong product of graphs over cycles and paths.