Note on group irregularity strength of disconnected graphs

Abstract

We investigate the \textit{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. So far it was not known if $s_g(G)$ is bounded for disconnected graphs. In the paper we we present some upper bound for all graphs. Moreover we give the exact values and bounds on $s_g(G)$ for disconnected graphs without a star as a component.

arXiv admin note: substantial text overlap with arXiv:1209.0200

References in corpus (1)

• Zero sum partition into sets of the same order and its applications

Cited by in corpus (1)

• Linear bounds on nowhere-zero group irregularity strength and nowhere-zero group sum chromatic number of graphs