On Spectral Graph Determination
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/4/549 |
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| _version_ | 1849722391747362816 |
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| author | Igal Sason Noam Krupnik Suleiman Hamud Abraham Berman |
| author_facet | Igal Sason Noam Krupnik Suleiman Hamud Abraham Berman |
| author_sort | Igal Sason |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9e6a2e8fbcf94cd899cccdf324cb5e8f |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-9e6a2e8fbcf94cd899cccdf324cb5e8f2025-08-20T03:11:21ZengMDPI AGMathematics2227-73902025-02-0113454910.3390/math13040549On Spectral Graph DeterminationIgal Sason0Noam Krupnik1Suleiman Hamud2Abraham Berman3Department of Electrical and Computer Engineering, Technion—Israel Institute of Technology, Haifa 3200003, IsraelDepartment of Computer Science, Technion—Israel Institute of Technology, Haifa 3200003, IsraelDepartment of Mathematics, Technion—Israel Institute of Technology, Haifa 3200003, IsraelDepartment of Mathematics, Technion—Israel Institute of Technology, Haifa 3200003, IsraelThe 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.https://www.mdpi.com/2227-7390/13/4/549spectral graph theoryspectral graph determinationcospectral nonisomorphic graphsHaemers’ conjectureTurán graphsgraph operations |
| spellingShingle | Igal Sason Noam Krupnik Suleiman Hamud Abraham Berman On Spectral Graph Determination Mathematics spectral graph theory spectral graph determination cospectral nonisomorphic graphs Haemers’ conjecture Turán graphs graph operations |
| title | On Spectral Graph Determination |
| title_full | On Spectral Graph Determination |
| title_fullStr | On Spectral Graph Determination |
| title_full_unstemmed | On Spectral Graph Determination |
| title_short | On Spectral Graph Determination |
| title_sort | on spectral graph determination |
| topic | spectral graph theory spectral graph determination cospectral nonisomorphic graphs Haemers’ conjecture Turán graphs graph operations |
| url | https://www.mdpi.com/2227-7390/13/4/549 |
| work_keys_str_mv | AT igalsason onspectralgraphdetermination AT noamkrupnik onspectralgraphdetermination AT suleimanhamud onspectralgraphdetermination AT abrahamberman onspectralgraphdetermination |