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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.)
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