On \delta^(k)-colouring of Powers of Paths and Cycles

Authors

Merlin Thomas Ellumkalayil Ms, Christ University, BangaloreFollow
Sudev Naduvath, Christ University, BangaloreFollow

Abstract

In an improper vertex colouring of a graph, adjacent vertices are permitted to receive same colours. An edge of an improperly coloured graph is said to be a bad edge if its end vertices have the same colour. A near-proper colouring of a graph is a colouring which minimises the number of bad edges by restricting the number of colour classes that can have adjacency among their own elements. The δ (k) - colouring is a near-proper colouring of G consisting of k given colours, where 1 ≤ k ≤ χ(G) – 1, which minimises the number of bad edges by permitting at most one colour class to have adjacency among the vertices in it. In this paper, we discuss the number of bad edges of powers of paths and cycles.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Ellumkalayil, Merlin Thomas Ms and Naduvath, Sudev (2021) "On \delta^(k)-colouring of Powers of Paths and Cycles," Theory and Applications of Graphs: Vol. 8: Iss. 2, Article 3.
DOI: 10.20429/tag.2021.080203
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol8/iss2/3