26.03.2012 Lecturer: dr. Marcin Anholcer (Poznan Univeristy of Economics, Poland)

Title: Group irregularity strength of graphs.

Abstract: 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. We prove that for any connected graph $G$ of order at least $3$, $s_\mathcal{G} (G)=n$ if $n\neq 4k+2$ and $s_\mathcal{G} (G)\leq n+1$ otherwise, except the case of some infinite family of stars.

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