Year: 2025
Type: article
Abstract: A divisor graph Gn of a positive integer n is a simple graph with vertices as proper divisors of n, in which two distinct divisors are adjacent if and only if they are relatively prime. Also G′n is a graph with vertices as divisors of n except n, such that the two distinct vertices are adjacent if and only if their greatest common divisor is one. These graph play a fundamental role in the study of the comaximal graphs associated to commutative rings. We study the graph theoretic properties of both Gn and G′n. Formally, we determine the clique number, the independence number, the chromatic number and the automorphism group of the divisor graphs Gn and G′n. We also find the bounds for their metric dimension along with the characterization of graphs attaining them. Further, we discuss their resolving polynomial.
Source: RAIRO - Operations Research
DOI: 10.1051/ro/2025030
Authors: Bilal Ahmad Rather, Hilal A. Ganie
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408730707