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- W3157431921 abstract "A proper edge $k$-colouring of a graph $G=(V,E)$ is an assignment $c:Eto {1,2,ldots,k}$ of colours to the edges of the graph such that no two adjacent edges are associated with the same colour. A neighbour sum distinguishing edge $k$-colouring, or nsd $k$-colouring for short, is a proper edge $k$-colouring such that $sum_{eni u}c(e)neq sum_{eni v}c(e)$ for every edge $uv$ of $G$. We denote by $chi'_{sum}(G)$ the neighbour sum distinguishing index of $G$, which is the least integer $k$ such that an nsd $k$-colouring of $G$ exists. By definition at least maximum degree, $Delta(G)$ colours are needed for this goal. In this paper we prove that $chi'_Sigma(G) leq Delta(G)+1$ for any graph $G$ without isolated edges and with ${rm mad}(G)<3$, $Delta(G) geq 6$." @default.
- W3157431921 created "2021-05-10" @default.
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- W3157431921 date "2017-06-13" @default.
- W3157431921 modified "2023-10-16" @default.
- W3157431921 title "On the Neighbour Sum Distinguishing Index of Graphs with Bounded Maximum Average Degree" @default.
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- W3157431921 doi "https://doi.org/10.1007/s00373-017-1822-3" @default.
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