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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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