Speaker
Kate Lorenzen
(Linfield University)
Description
Graphs can be encoded into a matrix according to some rule. The eigenvalues of the matrix are used to understand the structural properties of graphs. If two graphs share a set of eigenvalues, they are called cospectral. A tree is a graph with no cycles, and for most matrix representations, almost all trees have a cospectral mate. The distance Laplacian matrix is found by subtracting the distance matrix from the diagonal transmission matrix. There is an open conjecture that trees, for their distance Laplacian matrices, do not have a cospectral mate and are therefore spectrally determined. We explicitly find the spectrum of a family of trees of diameter 4 and how it is uniquely defined by its parameters.
Author
Kate Lorenzen
(Linfield University)