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Note on group irregularity strength of disconnected graphs. (English) Zbl 1390.05200
Summary: We investigate the group irregularity strength (\(s_g(G)\)) of graphs, i.e. the smallest value of \(s\) such that taking any abelian group of order \(s\), there exists a function \(f : E(G) \rightarrow \mathcal{G}\) such that the sums of edge labels at every vertex are distinct. So far it was not known if \(s_g(G)\) is finite for disconnected graphs. In the paper 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.

MSC:
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C22 Signed and weighted graphs
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