Year: 2025
Type: article
Abstract: Let R=M_2(F), where F is a finite field. In this paper, we investigate the idempotent graph of a ring R denoted by I*(R). We demonstrate that I*(R) is disconnected, having the components either complete bipartite graphs or complete graphs. A characterization is obtained for the regularity of I*(R). We determine the adjacency and Laplacian spectrum, the energy of I*(R) and prove Beck's conjecture.
Source: Gulf Journal of Mathematics
Authors: Anita Lande, Anil Khairnar
Institution: Abasaheb Garware College
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409608628