Graphs that are cospectral for the distance Laplacian
Date
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
Journal Issue
Is Version Of
Versions
Series
Department
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." The Electronic Journal of Linear Algebra 36, no. 36 (2020): 334-351. DOI: 10.13001/ela.2020.4941. Posted with permission.