Group irregularity strength of disconnected graphs

Abstract

We investigate the \textit{group irregular strength} $(s_g(G))$ of graphs, i.e the smallest value of $s$ such that for any Abelian group $\Gamma$ of order $s$ exists a function $g:E(G)\to \Gamma$ 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.

6 pages, 1 figure

References in corpus (2)

• Linear bounds on nowhere-zero group irregularity strength and nowhere-zero group sum chromatic number of graphs
• Realization of digraphs in Abelian groups and its consequences