Coprime divisors graphs and their coloring parameters

Mohamed Jorf; Brahim Boudine; Lahcen Oukhtite

doi:10.47443/dml.2024.045

Author(s)

Mohamed Jorf Department of Mathematics, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University,Fez,Morocco

Brahim Boudine Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University,Fez,Morocco

Lahcen Oukhtite Department of Mathematics, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University,Fez,Morocco

Abstract

Let n be a composite integer. The coprime divisors graph of n, denoted by n, is the graph whose vertices are the proper divisors of n and two vertices are adjacent if they are coprime. In this paper, we study the structure of n and its coloring parameters. Indeed, we give the explicit forms of the degrees, distances, diameter, and girth of this graph. We also compute explicitly the clique number, the chromatic number, and the independence number of n. Moreover, we prove that n is a perfect graph.

Publication Details

Page(s) 128-134

DOI 10.47443/dml.2024.045

Published Journal: Discrete Mathematics Letters, Volume: 13, Issue: 0, Year: 2024

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Keywords

chromatic number, divisors, perfect graph, independence number

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