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- W4301708389 abstract "A proper total $k$-colouring of a graph $G=(V,E)$ is an assignment $c : V cup Eto {1,2,ldots,k}$ of colours to the edges and the vertices of $G$ such that no two adjacent edges or vertices and no edge and its end-vertices are associated with the same colour. A total neighbour sum distinguishing $k$-colouring, or tnsd $k$-colouring for short, is a proper total $k$-colouring such that $sum_{eni u}c(e)+c(u)neq sum_{eni v}c(e)+c(v)$ for every edge $uv$ of $G$. We denote by $chi''_{Sigma}(G)$ the total neighbour sum distinguishing index of $G$, which is the least integer $k$ such that a tnsd edge $k$-colouring of $G$ exists. It has been conjectured that $chi''_{Sigma}(G) leq Delta(G) + 3$ for every graph $G$. In this paper we confirm this conjecture for any graph $G$ with ${rm mad}(G)<frac{14}{3}$ and $Delta(G) geq 8$." @default.
- W4301708389 created "2022-10-05" @default.
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- W4301708389 date "2018-03-05" @default.
- W4301708389 modified "2023-10-14" @default.
- W4301708389 title "On the total neighbour sum distinguishing index of graphs with bounded maximum average degree" @default.
- W4301708389 doi "https://doi.org/10.48550/arxiv.1803.02686" @default.
- W4301708389 hasPublicationYear "2018" @default.
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