Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

6-8-2020

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

36

Issue

36

First Page

334

Last Page

351

DOI

10.13001/ela.2020.4941

Abstract

The distance matrix D(G) of a graph G is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is DL(G)=T(G)−D(G), where T(G) is the diagonal matrix of row sums of D(G). We establish several general methods for producing DL-cospectral graphs that can be used to construct infinite families. We provide examples showing that various properties are not preserved by DL-cospectrality, including examples of DL-cospectral strongly regular and circulant graphs. We establish that the absolute values of coefficients of the distance Laplacian characteristic polynomial are decreasing, i.e., |δL1|≥⋯≥|δLn| where δLk is the coefficient of xk.

Comments

This article is published as Brimkov, Boris, Ken Duna, Leslie Hogben, Kate Lorenzen, Carolyn Reinhart, Sung-Yell Song, and Mark Yarrow. "Graphs that are cospectral for the distance Laplacian." 36, no. 36 The Electronic Journal of Linear Algebra (2020): 334-351. DOI: 10.13001/ela.2020.4941. Posted with permission.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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