Close-to-zero eigenvalues of the rooted product of graphs
type: Item
instance of: scholarly article
title: Close-to-zero eigenvalues of the rooted product of graphs
zbMATH Open document ID: 1478.92263
author: Vladimir R. Rosenfeld
author: Yujun Yang
publication date: 2021-07-07T00:00:00Z
review text: In the quantum chemistry the energy gap refers to the energy of an electron in the HOMO-LUMO transfer. The energy gap is the difference between the smallest positive \(\lambda_+\) and the largest negative eigenvalue \(\lambda_-\) of the adjacency matrix of the associated molecular graph. In this paper the authors use a rooted product of two graphs \(G\) and \(H\) denoted \(G(H)\) and they name it a vertex-decorated graph. The main idea is to choose graph \(H\) for a given graph \(G\) in such a way that the close to zero eigenvalues \(\lambda_+\) and \(\lambda_-\) of the rooted product \(G(H)\) give the smallest difference. For a certain family of graphs the characterization of obtaining a close to zero energy gap is given. The method is presented on four examples.
Mathematics Subject Classification ID: 92E10
Mathematics Subject Classification ID: 05C92
zbMATH DE Number: 7369403
zbMATH Keywords: rooted product of graphs
zbMATH Keywords: median eigenvalues
zbMATH Keywords: energy gap
reviewed by: Petra Žigert
MaRDI profile type: Publication
full work available at URL: s10910-021-01250-6
OpenAlex ID: W3161550871
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DOI: 10.1007/S10910-021-01250-6
published in: Journal of Mathematical Chemistry
description: scientific article; zbMATH DE number 7369403