On the adjacency matrix of a threshold graph

被引：31
|
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
收藏
页码：3008 / 3015
页数：8
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