7 papers · 1 filter
A cospectral construction for the generalized distance matrix
Ori Friesen, Cecily Kolko, Nick Layman +3
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 o…
Defective eigenvalues of the non-backtracking matrix
Kristin Heysse, Kate Lorenzen, Carolyn Reinhart
We consider graphs for which the non-backtracking matrix has defective eigenvalues, or graphs for which the matrix does not have a full set of eigenvectors. The existence of these…
On the Edge Derivative of the Normalized Laplacian with Applications to Kemeny's Constant
Connor Albright, Kimberly P. Hadaway, Ari Holcombe Pomerance +3
In a connected graph, Kemeny's constant gives the expected time of a random walk from an arbitrary vertex to reach a randomly-chosen vertex . Because of this, Kemeny's const…
Cospectral constructions for several graph matrices using cousin vertices
Kate Lorenzen
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same s…
Spectral properties of the exponential distance matrix
Steve Butler, Elizabeth Coper, Aaron Li +2
Given a graph , the exponential distance matrix is defined entry-wise by letting the -entry be , where is the distance between th…
Graphs that are cospectral for the distance Laplacian
Boris Brimkov, Ken Duna, Leslie Hogben +4
The distance matrix of a graph is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is $\mathcal{D}^L(G)=T(G)-\m…