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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
Abstract

Given a graph G, the exponential distance matrix is defined entrywise by letting the (u,v)-entry be qdist (u,v) , where dist (u,v) is the distance between the vertices u and v with the convention that if vertices are in different components, then qdist (u,v) = 0. 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
Mathematical Subject Classification 2010
Primary: 05C50
Milestones
Received: 13 October 2019
Revised: 18 January 2022
Accepted: 31 January 2022
Published: 3 March 2023

Communicated by Kenneth S. Berenhaut
Authors
Steve Butler
Department of Mathematics
Iowa State University
Ames, IA
United States
Elizabeth Cooper
Brooklyn, NY
United States
Aaron Li
University of Minnesota
Minneapolis, MN
United States
Kate Lorenzen
Linfield University
McMinville, OR
United States
Zoë Schopick
Tucson, AZ
United States