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- W2595589566 abstract "Consider a positive integer $r$ and a graph $G=(V,E)$ with maximum degree $Delta$ and without isolated edges. The least $k$ so that a proper edge colouring $c:Eto{1,2,ldots,k}$ exists such that $sum_{eni u}c(e)neq sum_{eni v}c(e)$ for every pair of distinct vertices $u,v$ at distance at most $r$ in $G$ is denoted by $chi'_{Sigma,r}(G)$. For $r=1$ it has been proved that $chi'_{Sigma,1}(G)=(1+o(1))Delta$. For any $rgeq 2$ in turn an infinite family of graphs is known with $chi'_{Sigma,r}(G)=Omega(Delta^{r-1})$. We prove that on the other hand, $chi'_{Sigma,r}(G)=O(Delta^{r-1})$ for $rgeq 2$. In particular we show that $chi'_{Sigma,r}(G)leq 6Delta^{r-1}$ if $rgeq 4$." @default.
- W2595589566 created "2017-03-23" @default.
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- W2595589566 date "2017-10-01" @default.
- W2595589566 modified "2023-10-01" @default.
- W2595589566 title "Distant sum distinguishing index of graphs" @default.
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- W2595589566 doi "https://doi.org/10.1016/j.disc.2017.05.009" @default.
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