On Spectral Graph Determination

Igal Sason; Noam Krupnik; Suleiman Hamud; Abraham Berman

doi:https://doi.org/10.3390/math13040549

On Spectral Graph Determination

Igal Sason, Noam Krupnik, Suleiman Hamud, Abraham Berman

Technion - Israel Institute of Technology

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

Abstract

The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing the conditions under which a graph’s spectrum uniquely determines its structure. This paper presents an overview of both classical and recent advancements in these topics, along with newly obtained proofs of some existing results, which offer additional insights.

Original language	English
Article number	549
Journal	Mathematics
Volume	13
Issue number	4
DOIs	https://doi.org/10.3390/math13040549
State	Published - Feb 2025

Keywords

Haemers’ conjecture
Turán graphs
cospectral nonisomorphic graphs
graph operations
spectral graph determination
spectral graph theory

All Science Journal Classification (ASJC) codes

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

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Cite this

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title = "On Spectral Graph Determination",

abstract = "The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing the conditions under which a graph{\textquoteright}s spectrum uniquely determines its structure. This paper presents an overview of both classical and recent advancements in these topics, along with newly obtained proofs of some existing results, which offer additional insights.",

keywords = "Haemers{\textquoteright} conjecture, Tur{\'a}n graphs, cospectral nonisomorphic graphs, graph operations, spectral graph determination, spectral graph theory",

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AU - Krupnik, Noam

AU - Hamud, Suleiman

AU - Berman, Abraham

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N2 - The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing the conditions under which a graph’s spectrum uniquely determines its structure. This paper presents an overview of both classical and recent advancements in these topics, along with newly obtained proofs of some existing results, which offer additional insights.

AB - The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods to construct or distinguish cospectral nonisomorphic graphs, and analyzing the conditions under which a graph’s spectrum uniquely determines its structure. This paper presents an overview of both classical and recent advancements in these topics, along with newly obtained proofs of some existing results, which offer additional insights.

KW - Haemers’ conjecture

KW - Turán graphs

KW - cospectral nonisomorphic graphs

KW - graph operations

KW - spectral graph determination

KW - spectral graph theory

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VL - 13

JO - Mathematics

JF - Mathematics

IS - 4

M1 - 549

ER -

On Spectral Graph Determination

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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