Journal or Book Title
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.
Brimkov, Boris; Duna, Ken; Hogben, Leslie; Lorenzen, Kate; Reinhart, Carolyn; Song, Sung-Yell; and Yarrow, Mark, "Graphs that are cospectral for the distance Laplacian" (2018). Mathematics Publications. 201.