Graphs with the same determinant as a complete graph
type: Item
instance of: scholarly article
title: Graphs with the same determinant as a complete graph
zbMATH Open document ID: 0958.05089
DOI: 10.1016/S0024-3795(00)00114-2
published in: Linear Algebra and its Applications
publication date: 2001-03-30T00:00:00Z
review text: It is well known that the determinant of the adjacency matrix of a complete graph \(K_n\) is equal to \((-1)^{n-1}(n-1)\). Recently it has been conjectured by \textit{X. Yong} [Linear Algebra Appl. 295, No. 1-3, 73-80 (1999; Zbl 0931.05056)] that \(K_n\) is the only class of graphs with such property. In the paper under review a family of symmetric circulant \((0,1)\)-matrices is studied. Each matrix in the family generates a graph that forms a counterexample to the conjecture. Eigenvalues of these matrices have an interesting octet structure.
reviewed by: Valeriy B. Mnukhin
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 1485566
zbMATH Keywords: complete graph
zbMATH Keywords: adjacency matrix
zbMATH Keywords: eigenvalues
zbMATH Keywords: determinant
zbMATH Keywords: circulant
author: D. D. Olesky
author: P. van den Driessche
author: James H. Verner
MaRDI profile type: Publication
cites work: Q4770409
cites work: Combinatorial matrix theory
cites work: Q3907599
cites work: Combinatorial Matrices with Small Determinants
cites work: On the distribution of eigenvalues of a simple undirected graph
full work available at URL: s0024-3795(00)00114-2
OpenAlex ID: W2053989944
description: scientific article; zbMATH DE number 1485566