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Spectral
properties of the exponential distance matrix
Steve Butler, Elizabeth Cooper, Aaron Li, Kate Lorenzen and Zoë Schopick
Vol. 15 (2022), No. 5, 739–762
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Abstract |
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Given a graph , the exponential distance matrix is defined entrywise by letting the -entry be , where is the distance between the vertices and with the convention that if vertices are in different components, then . We will establish several properties of the characteristic polynomial (spectrum) for this matrix, give some families of graphs which are uniquely determined by their spectrum, and produce cospectral constructions. |
Keywords
exponential distance matrix, spectral graph theory,
Cartesian product, cospectral graphs
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Mathematical Subject Classification 2010
Primary: 05C50
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Milestones
Received: 13 October 2019
Revised: 18 January 2022
Accepted: 31 January 2022
Published: 3 March 2023
Communicated by Kenneth S. Berenhaut
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Authors |
| Steve Butler | |
| Department of Mathematics Iowa State University Ames, IA United States |
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| Elizabeth Cooper | |
| Brooklyn, NY United States |
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| Aaron Li | |
| University of Minnesota Minneapolis, MN United States |
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| Kate Lorenzen | |
| Linfield University McMinville, OR United States |
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| Zoë Schopick | |
| Tucson, AZ United States |
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