@article {
author = {Naduvath, Sudev and Ellumkalayil, Merlin},
title = {A note on δ^(k)-colouring of the Cartesian product of some graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {7},
number = {1},
pages = {113-120},
year = {2022},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2021.27114.1211},
abstract = {The chromatic number, $\chi(G)$ of a graph $G$ is the minimum number of colours used in a proper colouring of $G$. In an improper colouring, an edge $uv$ is bad if the colours assigned to the end vertices of the edge is the same. Now, if the available colours are less than that of the chromatic number of graph $G$, then colouring the graph with the available colours lead to bad edges in $G$. The number of bad edges resulting from a $\delta^{(k)}$-colouring of $G$ is denoted by $b_{k}(G)$. In this paper, we use the concept of $\delta^{(k)}$-colouring and determine the number of bad edges in Cartesian product of some graphs.},
keywords = {Improper colouring,near proper colouring,δ^(k)-colouring,bad edge},
url = {http://comb-opt.azaruniv.ac.ir/article_14225.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_14225_7671b9be902fe5288eaea7c2a4aa2762.pdf}
}