On Zero-Divisor Graph of the ring 𝔽_p+u𝔽_p+u^2 𝔽_p

08/11/2022
∙
by   N. Annamalai, et al.
∙
0
∙

In this article, we discussed the zero-divisor graph of a commutative ring with identity 𝔽_p+u𝔽_p+u^2 𝔽_p where u^3=0 and p is an odd prime. We find the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth of a zero-divisor graph associated with the ring. We find some of topological indices and the main parameters of the code derived from the incidence matrix of the zero-divisor graph Γ(R). Also, we find the eigenvalues, energy and spectral radius of both adjacency and Laplacian matrices of Γ(R).

READ FULL TEXT

page 1

page 2

page 3

page 4

∙ 06/30/2020

Zero-divisors of content algebras

In this article, we prove that in content extensions minimal primes exte...
∙ 06/30/2020

Zero-divisor graphs of nilpotent-free semigroups

We find strong relationships between the zero-divisor graphs of apparent...
∙ 04/23/2023

On the Characterization of Regular Ring Lattices and their Relation with the Dirichlet Kernel

Regular ring lattices (RRLs) are defined as peculiar undirected circulan...
∙ 11/03/2020

Codes from the Incidence Matrices of a zero-divisor Graphs

In this paper, we examine the linear codes with respect to the Hamming m...
∙ 01/12/2023

Spectral properties of the Laplacian of temporal networks following a constant block Jacobi model

We study the behavior of the eigenvectors associated with the smallest e...
∙ 08/05/2017

The strong ring of simplicial complexes

We define a ring R of geometric objects G generated by finite abstract s...
∙ 11/22/2018

Second-Order Agents on Ring Digraphs

The paper addresses the problem of consensus seeking among second-order ...

Please sign up or login with your details

Forgot password? Click here to reset