Group irregularity strength of disconnected graphs

We investigate the $\mathit{\text{group}}\mathit{\text{irregular}}\mathit{\text{strength}}$ $(s_g(G))$ of graphs, i.e the smallest value of $s$ such that for any Abelian group $\mathrm{\Gamma }$ of order $s$ exists a function $g\text{\hspace{0.17em}⁣}:E(G)\to \mathrm{\Gamma }$ such that sums of edge labels at every vertex is distinct. We give results for bound and exact values of $(s_g(G))$ for graphs without small stars as components.