Note on the group edge irregularity strength of graphs

Abstract

We investigate the edge group irregularity strength (es g (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 upper bounds on es g (G) as well as for edge irregularity strength es(G) and harmonious order har(G).