Year: 2025
Type: article
Abstract: Let [Formula: see text] denote the coprime graph having vertex set [Formula: see text] with any two vertices [Formula: see text] being adjacent if and only if [Formula: see text]. In this paper, we first study some structural properties of [Formula: see text]. We study the vertex connectivity and crossing number of the coprime graph of integers. We discover a lower constraint on the multiplicity of [Formula: see text], which appears as an eigenvalue in the adjacency matrix of [Formula: see text]. We demonstrate our findings with a variety of cases. We also show that the adjacency matrix of [Formula: see text] is singular, i.e. has determinant [Formula: see text]. Furthermore, we give a lower bound on the multiplicity of [Formula: see text], which appears as an eigenvalue in the adjacency matrix of [Formula: see text]. Finally, we establish that the greatest eigenvalue of the adjacency matrix of [Formula: see text] is always above [Formula: see text].
Author: Subarsha Banerjee
Institution: JIS University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4411499345