For a graph X with at most one isolated vertex and without isolated edges, a product irregular labeling, is a labeling of its edges with the values from {1,2,…,s} in such a way that for any two distinct vertices u and v of X the product of labels of the edges incident with u is different from the product of labels of the edges incident with v. The minimal s for which there exist a product irregular labeling is called the product irregularity strength of X and is denoted by ps(X).

In this talk I will prove that  ps(X) ≤ |V(X)|-1, for any graph X with more than 3 vertices. I will also determine the product irregularity strength of the complete multipartite graphs.

This is a joint work with Ademir Hujdurović.