%0 Journal Article
%T Line graphs and the transplantation method
%A Peter Herbrich
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1504.02339v2