Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21287120220601A note on δ^(k)-colouring of the Cartesian product of some graphs1131201422510.22049/cco.2021.27114.1211ENSudevNaduvathChrist University, Bangalore, India.0000-0001-9692-4053Merlin ThomasEllumkalayilDepartment of Mathematics, Christ University, Bangalore, India.Journal Article20210323The 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.http://comb-opt.azaruniv.ac.ir/article_14225_7671b9be902fe5288eaea7c2a4aa2762.pdf