On ?(k)-colouring of Some Wheel Related Graphs

Title

On ?(k)-colouring of Some Wheel Related Graphs

Creator

Ellumkalayil M.T.; Naduvath S.; Jose S.

Description

The question on how to colour a graph G when the number of available colours to colour G is less than that of the chromatic number ?(G), such that the resulting colouring gives a minimum number of edges whose end vertices have the same colour, has been a study of great interest. Such an edge whose end vertices receives the same colour is called a bad edge. In this paper, we use the concept of ?(k)-colouring, where 1 ? k ? ?(G) ? 1, which is a near proper colouring that permits a single colour class to have adjacency between the vertices in it and restricts every other colour class to be an independent set, to find the minimum number of bad edges obtained from the same for some wheel related graphs. The minimum number of bad edges obtained from ?(k)-colouring of any graph G is denoted by bk(G). 2024 the Author(s), licensee Combinatorial Press.

Source

Journal of Combinatorial Mathematics and Combinatorial Computing, Vol-122, pp. 91-105.

Date

2024-01-01

Publisher

Charles Babbage Research Centre

Subject

Bad edges; Improper colouring; Near proper colouring; ?⁽k⁾-colouring

Coverage

Ellumkalayil M.T., Department of Mathematics, Christ University, Bangalore, 560029, India; Naduvath S., Department of Mathematics, Christ University, Bangalore, 560029, India; Jose S., Department of Mathematics, Christ University, Bangalore, 560029, India

Rights

All Open Access; Hybrid Gold Open Access

Relation

ISSN: 8353026

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.61091/jcmcc122-07

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