Characterizing Graphs with Nullity n−4

Raksha Poojary; Arathi K. Bhat; Manjunatha Prasad Karantha; S. Arumugam; Ivan Gutman

doi:10.46793/match.89-3.631P

Characterizing Graphs with Nullity n−4

Raksha Poojary
, Arathi K. Bhat
, Manjunatha Prasad Karantha^*
, S. Arumugam
, Ivan Gutman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	631-642
Number of pages	12
Journal	Match
Volume	89
Issue number	3
DOIs	https://doi.org/10.46793/match.89-3.631P
Publication status	Published - 2023

All Science Journal Classification (ASJC) codes

General Chemistry
Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

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title = "Characterizing Graphs with Nullity n−4",

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.",

author = "Raksha Poojary and Bhat, \{Arathi K.\} and Karantha, \{Manjunatha Prasad\} and S. Arumugam and Ivan Gutman",

note = "Funding Information: 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 Publisher Copyright: {\textcopyright} 2023 University of Kragujevac, Faculty of Science. All rights reserved.",

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doi = "10.46793/match.89-3.631P",

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T1 - Characterizing Graphs with Nullity n−4

AU - Poojary, Raksha

AU - Bhat, Arathi K.

AU - Karantha, Manjunatha Prasad

AU - Arumugam, S.

AU - Gutman, Ivan

N1 - Funding Information: 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 Publisher Copyright: © 2023 University of Kragujevac, Faculty of Science. All rights reserved.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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JO - Match

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Characterizing Graphs with Nullity n−4

Abstract

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