Remarks on hyperenergetic circulant graphs
type: Item
instance of: scholarly article
title: Remarks on hyperenergetic circulant graphs
zbMATH Open document ID: 1065.05064
author: Dragan Stevanović
author: Ivan Stanković
published in: Linear Algebra and its Applications
publication date: 2005-06-01T00:00:00Z
review text: The {energy} of a graph \(G\) is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of \(K_n\) is \(2(n-1)\). Motivated by a refuted conjecture that \(K_n\) is the graph of order \(n\) with maximum energy, graphs with energy greater than \(2(n-1)\) are called hyperenergetic. The circulant graph \(C(n,k_1,\dots,k_m)\) is the graph with vertex set \(\{0,\dots,n-1\}\) such that two of its vertices are joined by an edge if their difference modulo \(n\) is not equal to any of the numbers \(k_1,\dots,k_m\). The authors show that for every \(k_1,\dots,k_m\), there exists an integer \(n_0\) such that every circulant graph \(C(n,k_1,\dots,k_m)\) with \(n>n_0\) is hyperenergetic. This settles a problem of \textit{R. Balakrishnan} [Linear Algebra Appl. 387, 287--295 (2004; Zbl 1041.05046)] whether the complements of cycles are hyperenergetic.
reviewed by: Daniel Král'
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 2173036
zbMATH Keywords: spectrum of a graph
zbMATH Keywords: energy of a graph
zbMATH Keywords: eigenvalues
MaRDI profile type: Publication
full work available at URL: j.laa.2005.01.001
OpenAlex ID: W2028823949
cites work: The energy of a graph
cites work: Q5668821
cites work: Q4327350
cites work: Q4186355
DOI: 10.1016/J.LAA.2005.01.001
description: scientific article; zbMATH DE number 2173036