Note on the group edge irregularity strength of graphs

We investigate the textit{edge group irregularity strength} ($es_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $mathcal{G}$ of order $s$, there exists a function $f:V(G)rightarrow mathcal{G}$ 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 $rm{har}(G)$.