Group Irregularity Strength of Connected Graphs

Abstract

We investigate the group irregularity strength ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\gr$ of order $s$, there exists a function $f:E(G)\rightarrow \gr$ such that the sums of edge labels at every vertex are distinct. We prove that for any connected graph $G$ of order at least 3, $s_g(G)=n$ if $n\ne 4k+2$ and $s_g(G)\le n+1$ otherwise, except the case of some infinite family of stars.

References in corpus (1)

• Group Sum Chromatic Number of Graphs

Cited by in corpus (6)

• Zero-sum partitions of Abelian groups of order $2^n$
• Realization of digraphs in Abelian groups and its consequences
• Linear bounds on nowhere-zero group irregularity strength and nowhere-zero group sum chromatic number of graphs
• Note on group irregularity strength of disconnected graphs
• Group irregularity strength of disconnected graphs
• Note on the group edge irregularity strength of graphs