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The adjacency
spectra of some families of minimally connected prime
graphs
Chris Florez, Jonathan Higgins, Kyle Huang, Thomas Michael Keller and Dawei Shen |
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Vol. 17 (2024), No. 1, 107–120
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Abstract |
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In finite group theory, studying the prime graph of a group has been an important topic for almost the past half-century. Recently, prime graphs of solvable groups have been characterized in graph-theoretical terms only; this now allows the study of these graphs without any knowledge of the group-theoretical background. We approach prime graphs from a linear-algebraic angle and focus on the class of minimally connected prime graphs introduced in earlier work on the subject. As our main results, we prove new properties about the adjacency matrices of some special families of these graphs, focusing on their characteristic polynomials and spectra. |
Keywords
prime graphs, adjacency matrix, spectral graph theory
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Mathematical Subject Classification
Primary: 05C25, 15A18
Secondary: 20D10
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Milestones
Received: 29 August 2022
Revised: 10 December 2022
Accepted: 17 December 2022
Published: 15 March 2024
Communicated by Vadim Ponomarenko
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Authors |
| Chris Florez | |
| Department of Mathematics David Rittenhouse Lab University of Pennsylvania Philadelphia, PA United States |
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| Jonathan Higgins | |
| Department of Mathematics University of Illinois Urbana-Champaign Urbana, IL United States |
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| Kyle Huang | |
| Department of Mathematics Freie Universität Berlin Berlin Germany |
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| Thomas Michael Keller | |
| Department of Mathematics Texas State University San Marcos, TX United States |
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| Dawei Shen | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
