On the adjacency matrix of a threshold graph

被引：32

作者：

Bapat, R. B. ^{[1
]}

机构：

[1] Indian Stat Inst, Delhi Ctr, New Delhi 110016, India

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 439卷 / 10期

关键词：

Threshold graph; Antiregular graph; Adjacency matrix; Inertia;

D O I：

10.1016/j.laa.2013.08.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A threshold graph on n vertices is coded by a binary string of length n - 1. We obtain a formula for the inertia of (the adjacency matrix of) a threshold graph in terms of the code of the graph. It is shown that the number of negative eigenvalues of the adjacency matrix of a threshold graph is the number of ones in the code, whereas the nullity is given by the number of zeros in the code that are preceded by either a zero or a blank. A formula for the determinant of the adjacency matrix of a generalized threshold graph and the inverse, when it exists, of the adjacency matrix of a threshold graph are obtained. Results for antiregular graphs follow as special cases. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3008 / 3015

页数：8