TY - JOUR
ID - 14225
TI - A note on δ^(k)-colouring of the Cartesian product of some graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Naduvath, Sudev
AU - Ellumkalayil, Merlin Thomas
AD - Christ University, Bangalore, India.
AD - Department of Mathematics, Christ University, Bangalore, India.
Y1 - 2022
PY - 2022
VL - 7
IS - 1
SP - 113
EP - 120
KW - Improper colouring
KW - near proper colouring
KW - δ^(k)-colouring
KW - bad edge
DO - 10.22049/cco.2021.27114.1211
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14225.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14225_7671b9be902fe5288eaea7c2a4aa2762.pdf
ER -