Group Sum Chromatic Number of Graphs

Marcin Anholcer; Sylwia Cichacz

arXiv:1205.2572·math.CO·March 4, 2016·Eur. J. Comb.

Group Sum Chromatic Number of Graphs

Marcin Anholcer, Sylwia Cichacz

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Abstract

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

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