Universal adjacency spectrum of zero divisor graph on the ring and its complement

For a commutative ring R with unity, the zero divisor graph is an undirected graph with all non-zero zero divisors of R as vertices and two distinct vertices u and v are adjacent if and only if uv = 0. For a simple graph G with the adjacency matrix A and degree diagonal matrix D, the universal adjac...

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Autores principales:	Saraswati Bajaj, Pratima Panigrahi
Formato:	article
Lenguaje:	EN
Publicado:	Taylor & Francis Group 2021
Materias:	zero divisor graph universal adjacency matrix eigenvector eigenvalue complement Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0a6a157b0f6e4d7ca92c056d2e9950f8
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spelling	oai:doaj.org-article:0a6a157b0f6e4d7ca92c056d2e9950f82021-12-01T14:40:58ZUniversal adjacency spectrum of zero divisor graph on the ring and its complement0972-86002543-347410.1080/09728600.2021.2001701https://doaj.org/article/0a6a157b0f6e4d7ca92c056d2e9950f82021-11-01T00:00:00Zhttp://dx.doi.org/10.1080/09728600.2021.2001701https://doaj.org/toc/0972-8600https://doaj.org/toc/2543-3474For a commutative ring R with unity, the zero divisor graph is an undirected graph with all non-zero zero divisors of R as vertices and two distinct vertices u and v are adjacent if and only if uv = 0. For a simple graph G with the adjacency matrix A and degree diagonal matrix D, the universal adjacency matrix is where I is identity matrix and J is all-ones matrix. For a graph H on k vertices and a family of vertex disjoint regular graphs we determine eigenpairs of the universal adjacency matrix of H-join of in terms of eigenpairs of the adjacency matrix of Hi, and a symmetric matrix of order k. For a non-prime integer n > 3, we obtain eigenpairs of and As an application, we also discuss the adjacency, Seidel, Laplacian and signless Laplacian spectra of both and Lastly, we determine the characteristic polynomial of for prime p and integer m > 1 (except for with ).Saraswati BajajPratima PanigrahiTaylor & Francis Grouparticlezero divisor graphuniversal adjacency matrixeigenvectoreigenvaluecomplementMathematicsQA1-939ENAKCE International Journal of Graphs and Combinatorics, Vol 0, Iss 0, Pp 1-17 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	zero divisor graph universal adjacency matrix eigenvector eigenvalue complement Mathematics QA1-939
spellingShingle	zero divisor graph universal adjacency matrix eigenvector eigenvalue complement Mathematics QA1-939 Saraswati Bajaj Pratima Panigrahi Universal adjacency spectrum of zero divisor graph on the ring and its complement
description	For a commutative ring R with unity, the zero divisor graph is an undirected graph with all non-zero zero divisors of R as vertices and two distinct vertices u and v are adjacent if and only if uv = 0. For a simple graph G with the adjacency matrix A and degree diagonal matrix D, the universal adjacency matrix is where I is identity matrix and J is all-ones matrix. For a graph H on k vertices and a family of vertex disjoint regular graphs we determine eigenpairs of the universal adjacency matrix of H-join of in terms of eigenpairs of the adjacency matrix of Hi, and a symmetric matrix of order k. For a non-prime integer n > 3, we obtain eigenpairs of and As an application, we also discuss the adjacency, Seidel, Laplacian and signless Laplacian spectra of both and Lastly, we determine the characteristic polynomial of for prime p and integer m > 1 (except for with ).
format	article
author	Saraswati Bajaj Pratima Panigrahi
author_facet	Saraswati Bajaj Pratima Panigrahi
author_sort	Saraswati Bajaj
title	Universal adjacency spectrum of zero divisor graph on the ring and its complement
title_short	Universal adjacency spectrum of zero divisor graph on the ring and its complement
title_full	Universal adjacency spectrum of zero divisor graph on the ring and its complement
title_fullStr	Universal adjacency spectrum of zero divisor graph on the ring and its complement
title_full_unstemmed	Universal adjacency spectrum of zero divisor graph on the ring and its complement
title_sort	universal adjacency spectrum of zero divisor graph on the ring and its complement
publisher	Taylor & Francis Group
publishDate	2021
url	https://doaj.org/article/0a6a157b0f6e4d7ca92c056d2e9950f8
work_keys_str_mv	AT saraswatibajaj universaladjacencyspectrumofzerodivisorgraphontheringanditscomplement AT pratimapanigrahi universaladjacencyspectrumofzerodivisorgraphontheringanditscomplement
_version_	1718405039371845632

Universal adjacency spectrum of zero divisor graph on the ring and its complement

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