Group Sum Chromatic Number of Graphs
arXiv:1205.2572 · doi:10.1016/j.ejc.2016.02.002
Abstract
We investigate the \textit{group sum chromatic number} ($\gchi(G)$) of graphs, i.e. the smallest value such that taking any Abelian group $\gr$ of order , there exists a function $f:E(G)\rightarrow \gr$ 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 with no component of order less than and we characterize the graphs for which $\gchi(G)=χ(G)$.
arXiv commentAccepted for publication in European Journal of Combinatorics, Elsevier