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Line graphs and the transplantation method

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.

preprint2015arXivOpen access
Peter Herbrich
math.COmath.SP
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Peter Herbrich

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