Note on the group edge irregularity strength of graphs

Abstract

We investigate the group edge irregularity strength (esg(G)) of graphs, i.e. the smallest value of s such that taking any Abelian group G of order s, there exists a function f:V(G)→G such that the sums of vertex labels at every edge are distinct. In this note we provide some the upper bounds on esg(G) as well as for edge irregularity strength es(G) and harmonious order har(G).