# Distant sum distinguishing index of graphs with bounded minimum degree

@inproceedings{Przybyo2017DistantSD, title={Distant sum distinguishing index of graphs with bounded minimum degree}, author={Jakub Przybyło}, year={2017} }

- Published 2017
DOI:10.26493/1855-3974.1496.623

For any graph $G=(V,E)$ with maximum degree $\Delta$ and without isolated edges, and a positive integer $r$, by $\chi'_{\Sigma,r}(G)$ we denote the $r$-distant sum distinguishing index of $G$. This is the least integer $k$ for which a proper edge colouring $c:E\to\{1,2,\ldots,k\}$ exists such that $\sum_{e\ni u}c(e)\neq \sum_{e\ni v}c(e)$ for every pair of distinct vertices $u,v$ at distance at most $r$ in $G$. It was conjectured that $\chi'_{\Sigma,r}(G)\leq (1+o(1))\Delta^{r-1}$ for every $r… CONTINUE READING