Line graphs and the transplantation method
Spectral Theory
2015-04-14 v2 Combinatorics
Abstract
We study isospectrality for mixed Dirichlet-Neumann boundary conditions, and extend the previously derived graph-theoretic formulation of the transplantation method. Led by the theory of Brownian motion, we introduce vertex-colored and edge-colored line graphs that give rise to block diagonal transplantation matrices. In particular, we rephrase the transplantation method in terms of representations of free semigroups, and provide a method for generating adjacency cospectral weighted directed graphs.
Cite
@article{arxiv.1504.02339,
title = {Line graphs and the transplantation method},
author = {Peter Herbrich},
journal= {arXiv preprint arXiv:1504.02339},
year = {2015}
}
Comments
8 pages, 1 figure