Group sum chromatic number of graphs

We investigate the group sum chromatic number ( ? g Σ ( G ) ) of graphs, i.e. the smallest value s such that taking any Abelian group G of order s , there exists a function f : E ( G ) ? G such that the sums of edge labels properly colour the vertices. It is known that ? g Σ ( G ) ? { ? ( G ) , ? ( G ) + 1 } for any graph G with no component of order less than 3 and we characterize the graphs for which ? g Σ ( G ) = ? ( G ) .

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