On the spectrum and energy of singular graphs

On the spectrum and energy of singular graphs

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Energy of a graph is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix A(G)of a graph Gand is denoted by E(G). The graph G with n vertices is called nonhypoenergetic if E(G)≥nand hypoenergetic if E(G)<n. Singular graphs are graphs with nullity η(G)>0. In this...

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Main Authors: T.K. Mathew Varkey, John K. Rajan
Format: Article
Language:English
Published: Taylor & Francis Group 2019-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Online Access:http://www.sciencedirect.com/science/article/pii/S0972860016301608
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spelling doaj-77595b4920a84362af8fa23252af94672020-11-25T02:58:17ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163265271On the spectrum and energy of singular graphsT.K. Mathew Varkey0John K. Rajan1Department of Mathematics, TKM College of Engineering, Kollam, Kerala, India; Corresponding author.Department of Mathematics, University College, Thiruvananthapuram, Kerala, IndiaEnergy of a graph is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix A(G)of a graph Gand is denoted by E(G). The graph G with n vertices is called nonhypoenergetic if E(G)≥nand hypoenergetic if E(G)<n. Singular graphs are graphs with nullity η(G)>0. In this paper we study about nonhypoenergetic and hypoenergetic graphs among singular graphs. We also construct singular graphs of larger nullity using coalescence. Keywords: Singular graphs, Coalescence, Core vertices, Energy of graph, Nonhypoenergetic graphhttp://www.sciencedirect.com/science/article/pii/S0972860016301608
collection DOAJ
language English
format Article
sources DOAJ
author T.K. Mathew Varkey
John K. Rajan
spellingShingle T.K. Mathew Varkey
John K. Rajan
On the spectrum and energy of singular graphs
AKCE International Journal of Graphs and Combinatorics
author_facet T.K. Mathew Varkey
John K. Rajan
author_sort T.K. Mathew Varkey
title On the spectrum and energy of singular graphs
title_short On the spectrum and energy of singular graphs
title_full On the spectrum and energy of singular graphs
title_fullStr On the spectrum and energy of singular graphs
title_full_unstemmed On the spectrum and energy of singular graphs
title_sort on the spectrum and energy of singular graphs
publisher Taylor & Francis Group
series AKCE International Journal of Graphs and Combinatorics
issn 0972-8600
publishDate 2019-12-01
description Energy of a graph is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix A(G)of a graph Gand is denoted by E(G). The graph G with n vertices is called nonhypoenergetic if E(G)≥nand hypoenergetic if E(G)<n. Singular graphs are graphs with nullity η(G)>0. In this paper we study about nonhypoenergetic and hypoenergetic graphs among singular graphs. We also construct singular graphs of larger nullity using coalescence. Keywords: Singular graphs, Coalescence, Core vertices, Energy of graph, Nonhypoenergetic graph
url http://www.sciencedirect.com/science/article/pii/S0972860016301608
work_keys_str_mv AT tkmathewvarkey onthespectrumandenergyofsingulargraphs
AT johnkrajan onthespectrumandenergyofsingulargraphs
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