On Spectral Graph Determination

Igal Sason (), Noam Krupnik, Suleiman Hamud and Abraham Berman
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Igal Sason: Department of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, Israel
Noam Krupnik: Department of Computer Science, Technion—Israel Institute of Technology, Haifa 3200003, Israel
Suleiman Hamud: Department of Mathematics, Technion—Israel Institute of Technology, Haifa 3200003, Israel
Abraham Berman: Department of Mathematics, Technion—Israel Institute of Technology, Haifa 3200003, Israel

Mathematics, 2025, vol. 13, issue 4, 1-44

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.

Keywords: spectral graph theory; spectral graph determination; cospectral nonisomorphic graphs; Haemers’ conjecture; Turán graphs; graph operations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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