dr. Marcin Anholcer – Group irregularity strength of graphs

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 $nneq 4k+2$ and $s_mathcal{G} (G)leq n+1$ otherwise, except the case of some infinite family of stars.

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