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MatchVolume 89, Issue 3, 2023, Pages 631-642

Characterizing Graphs with Nullity n−4(Article)(Open Access)

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  • aDepartment of Data Science, Prasanna School of Public Health, Manipal Academy of Higher Education, Karnataka, Manipal, 576104, India
  • bDepartment of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Karnataka, Manipal, 576104, India
  • cCenter for Advanced Research in Applied Mathematics and Statistics, Manipal Academy of Higher Education, Manipal, 576104, India
  • dDepartment of Computer Science and Engineering, Ramco Institute of Technology, Tamilnadu, Rajapalayam, 626117, India
  • eUniversity of Kragujevac, Kragujevac, Serbia

Abstract

The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of G. A unified approach is presented for the characterization of graphs of order n with η(G) = n − 4. All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and r-partite graphs, for which η(G) = n − 4 are shown to be corollaries of a theorem of Chang, Huang and Yeh that characterizes all graphs with nullity n − 4. © 2023 University of Kragujevac, Faculty of Science. All rights reserved.

Funding details

Funding sponsor Funding number Acronym
Department of Science and Technology, Ministry of Science and Technology, India
See opportunities by डीएसटी		CRG/2019/000238,MTR/2018/000156डीएसटी
Science and Engineering Research Board
See opportunities by SERB		SERB

  • 1

    Acknowledgment: Author Manjunatha Prasad Karantha acknowledge the support by Science and Engineering Research Board (DST), India through the projects CRG/2019/000238 and MTR/2018/000156

  • ISSN: 03406253
  • Source Type: Journal
  • Original language: English
  • DOI: 10.46793/match.89-3.631P
  • Document Type: Article
  • Publisher: University of Kragujevac, Faculty of Science

  Karantha, M.P.; Department of Data Science, Prasanna School of Public Health, Manipal Academy of Higher Education, Karnataka, Manipal, India;
© Copyright 2023 Elsevier B.V., All rights reserved.

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(2024) Discrete Mathematics
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