On the eigenvalues of zero-divisor graph associated to finite commutative ring
S. Pirzada, Bilal Ahmad Wani, A. Somasundaram
Abstract
Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by is a simple graph whose vertex set is and two vertices are adjacent if and only if In this paper, we investigate the adjacency matrix and the spectrum of the zero-divisor graphs for where are primes and M, N are positive integers. Moreover, we obtain the clique number, stability number and girth of
Topics & Concepts
MathematicsZero divisorCombinatoricsClique numberCommutative ringVertex (graph theory)Adjacency matrixZero (linguistics)Discrete mathematicsGraphSimple graphCommutative propertyLinguisticsPhilosophyRings, Modules, and AlgebrasAdvanced Topics in AlgebraFinite Group Theory Research