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
相关论文
共 50 条
  • [31] Contrastive Graph Convolutional Networks With Generative Adjacency Matrix
    Zhong, Luying
    Yang, Jinbin
    Chen, Zhaoliang
    Wang, Shiping
    IEEE Transactions on Signal Processing, 2023, 71 : 772 - 785
  • [32] SOME GRAPH INVARIANTS BASED IN THE EIGENVECTORS OF THE ADJACENCY MATRIX
    CVETKOVIC, DM
    GRAPH THEORY, 1989, : 31 - 42
  • [33] The adjacency matrix of a graph as a data table: a geometric perspective
    Chiaselotti, Giampiero
    Gentile, Tommaso
    Infusino, Federico G.
    Oliverio, Paolo A.
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2017, 196 (03) : 1073 - 1112
  • [34] Contrastive Graph Convolutional Networks With Generative Adjacency Matrix
    Zhong, Luying
    Yang, Jinbin
    Chen, Zhaoliang
    Wang, Shiping
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2023, 71 : 772 - 785
  • [35] Graph Representations using Adjacency Matrix Transforms for Clustering
    Tsapanos, Nikolaos
    Pitas, Ioannis
    Nikolaidis, Nikolaos
    2012 16TH IEEE MEDITERRANEAN ELECTROTECHNICAL CONFERENCE (MELECON), 2012, : 383 - 386
  • [36] An approach to solve graph coloring problem using adjacency matrix
    Shukla, Ajay Narayan
    Garg, M. L.
    BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS, 2019, 12 (02): : 472 - 477
  • [37] FPGA Acceleration of GCN in Light of the Symmetry of Graph Adjacency Matrix
    Nair, Gopikrishnan Raveendran
    Suh, Han-Sok
    Halappanavar, Mahantesh
    Liu, Frank
    Seo, Jae-Sun
    Cao, Yu
    Proceedings -Design, Automation and Test in Europe, DATE, 2023, 2023-April
  • [38] AOAM: Automatic Optimization of Adjacency Matrix for Graph Convolutional Network
    Zhang, Yuhang
    Ren, Hongshuai
    Ye, Jiexia
    Gao, Xitong
    Wang, Yang
    Ye, Kejiang
    Xu, Cheng-Zhong
    2020 25TH INTERNATIONAL CONFERENCE ON PATTERN RECOGNITION (ICPR), 2021, : 5130 - 5136
  • [39] On the number of minimal codewords in codes generated by the adjacency matrix of a graph
    Kurz, Sascha
    DISCRETE APPLIED MATHEMATICS, 2022, 309 : 221 - 228
  • [40] FPGA Acceleration of GCN in Light of the Symmetry of Graph Adjacency Matrix
    Nair, Gopikrishnan Raveendran
    Suh, Han-Sok
    Halappanavar, Mahantesh
    Liu, Frank
    Seo, Jae-Sun
    Cao, Yu
    2023 DESIGN, AUTOMATION & TEST IN EUROPE CONFERENCE & EXHIBITION, DATE, 2023,
12345