A cospectral construction for the generalized distance matrix
Abstract
The generalized distance matrix of a graph is a matrix in which the th entry is a function, , of the distance between vertex and vertex . Depending on the choice of , this family of matrices includes both the adjacency matrix and the traditional distance matrix. We present a cospectral construction for the generalized distance matrix akin to Godsil-McKay Switching. We also investigate a special case of the generalized distance matrix: the exponential distance matrix, which is a matrix where every entry is a value raised to the power of the distance between the vertices. We give an upper bound on the values of needed to show a pair of graphs is cospectral for all values of corresponding to the diameter of the graphs. We also give cospectral constructions unique to value .
Cite
@article{arxiv.2412.05389,
title = {A cospectral construction for the generalized distance matrix},
author = {Ori Friesen and Cecily Kolko and Nick Layman and Kate Lorenzen and Sarah Zaske and Amy Zeigler},
journal= {arXiv preprint arXiv:2412.05389},
year = {2024}
}