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Group irregularity strength of connected graphs. (English) Zbl 1316.05078
Summary: We investigate the group irregularity strength ($$s_g(G)$$) of graphs, that is, we find the minimum value of $$s$$ such that for any abelian group $$\mathcal G$$ of order $$s$$, there exists a function $$f:E(G)\to \mathcal G$$ 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 $$n\neq 4k+2$$ and $$s_g(G)\leq n+1$$ otherwise, except the case of an infinite family of stars. We also prove that the presented labelling algorithm is linear with respect to the order of the graph.
Reviewer: Reviewer (Berlin)

##### MSC:
 05C40 Connectivity 05C78 Graph labelling (graceful graphs, bandwidth, etc.)
##### Keywords:
irregularity strength; graph labelling; abelian group
Full Text:
##### References:
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