A cospectral construction for the generalized distance matrix
Year: 2025
Type: article
Abstract: The generalized distance matrix of a graph is a matrix in which the ( i , j ) \left(i,j) th entry is a function, f f , of the distance between vertex i i and vertex j j . Depending on the choice of f f , 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 q q raised to the power of the distance between the vertices. We give an upper bound on the values of q q needed to show a pair of graphs is cospectral for all values of q q corresponding to the diameter of the graphs. We also give cospectral constructions unique to value q = 1 ⁄ 2 q=1/2 .
Source: Special Matrices
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4412571791