Graphs and the Prime Spectrum of Unitary Commutative Rings

Abstract

In this paper, we study the relationships between graphs and the prime spectrum of unitary commutative rings. It is shown that a graph G equipped with the G-right topology satisfies some spectral properties. In particular we give a necessarily and sufficient condition to obtain a spectral graph.

Spectral Properties of Power Graph of Dihedral Groups

“…They worked on the spectral problem of the commuting and non-commuting graphs, which can be seen in [9][10][11][12][13], Accordingly, Romdhini et al [8] investigated signless Laplacian spectral of interval-valued fuzzy graphs. Moreover, an analysis of the relationship between graphs and unitary commutative rings' prime spectrum is presented by [1]. Motivated by this, this research aims to formulate the characteristic polynomial of the power graph of the dihedral group associated with the adjacency, Laplacian, signless Laplacian, and normalized form of these matrices.…”

Codimension One Foliation and the Prime Spectrum of a Ring

“…Recently, we study the relationships between graphs and the prime spectrum of unitary commutative rings [1].…”