Predavatelj: Marcin Anholcer

We investigate the textit{group irregularity strength} ($s_mathcal{G}(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $mathcal{G}$ of order $s$, there exists a function $f:E(G)rightarrow mathcal{G}$ such that the sums of edge labels in every vertex are distinct. In particular we prove that for any connected graph $G$ of order at least $3$, $s_mathcal{G} (G)=n$ if $nneq 4k+2$ and $s_mathcal{G} (G)leq n+1$ otherwise, except the case of some infinite family of stars. We investigate also the local version of the problem, this time we prove that $s=chi(G)$ or $s=chi(G)+1$ is enough with few exceptions.