Graphs with the same determinant as a complete graph

被引：3

作者：

Olesky, DD

van den Driessche, P

Verner, JH

机构：

[1] Univ Victoria, Dept Comp Sci, STN CSC, Victoria, BC V8W 3P6, Canada

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

[3] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 312卷 / 1-3期

基金：

加拿大自然科学与工程研究理事会;

关键词：

adjacency matrix; circulant; complete graph; determinant; eigenvalues;

D O I：

10.1016/S0024-3795(00)00114-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A family of n x n symmetric circulant (0, 1) matrices is studied. It is shown that the determinant of each matrix is (-1)(n-1)(n - 1), a property shared with the adjacency matrix of the complete graph on n nodes. As a result, each matrix in this family generates an incomplete graph that forms a counterexample to a recent conjecture. (C) 2000 Elsevier Science Inc. All rights reserved.

引用

页码：191 / 195

页数：5