Nullity of Graphs—A Survey and Some New Results

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

doi:10.1007/978-981-99-2310-6_8

Nullity of Graphs—A Survey and Some New Results

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

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter

3 Citations (Scopus)

Abstract

The spectrum of a graph G is the set of eigenvalues of the adjacency matrix of G. The nullity η(G), which is the algebraic multiplicity of the number zero in the spectrum of G, is a graph spectrum-based invariant. In the context of the H u. ckel Molecular Orbital theory, the nullity of a molecular graph is used to determine the stability of unsaturated conjugated hydrocarbons. In this paper, we present a survey of significant results on nullity, such as bounds, transformations preserving nullity, nullity of line graphs, nullity versus energy and graphs with high nullity, along with some new results.

Original language	English
Title of host publication	Indian Statistical Institute Series
Publisher	Springer Science and Business Media B.V.
Pages	155-175
Number of pages	21
DOIs	https://doi.org/10.1007/978-981-99-2310-6_8
Publication status	Published - 2023

Publication series

Name	Indian Statistical Institute Series
Volume	Part F1229
ISSN (Print)	2523-3114
ISSN (Electronic)	2523-3122

All Science Journal Classification (ASJC) codes

Computer Science (miscellaneous)
Statistics and Probability
Mathematics (miscellaneous)
Computer Science Applications
Statistics, Probability and Uncertainty
Applied Mathematics

Access to Document

10.1007/978-981-99-2310-6_8

Cite this

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title = "Nullity of Graphs—A Survey and Some New Results",

abstract = "The spectrum of a graph G is the set of eigenvalues of the adjacency matrix of G. The nullity η(G), which is the algebraic multiplicity of the number zero in the spectrum of G, is a graph spectrum-based invariant. In the context of the H u. ckel Molecular Orbital theory, the nullity of a molecular graph is used to determine the stability of unsaturated conjugated hydrocarbons. In this paper, we present a survey of significant results on nullity, such as bounds, transformations preserving nullity, nullity of line graphs, nullity versus energy and graphs with high nullity, along with some new results.",

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

note = "Funding Information: Acknowledgements Among the authors, Manjunatha Prasad Karantha wishes to acknowledge the funding support by Science and Engineering Research Board (DST), India, through the projects CRG/2019/000238 and MTR/2018/000156. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.",

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