  Construction of graphs with equal eigenvalues (co-spectral graphs) is an
interesting problem in spectral graph theory. Seidel switching is a well-known
method for generating co-spectral graphs. From a matrix theoretic point of
view, Seidel switching is a combined action of a number of unitary operations
on graphs. Recent works [1] and [2] have shown significant connections between
graph and quantum information theories. Corresponding to Laplacian matrices of
any graph there are quantum states useful in quantum computing. From this point
of view, graph theoretical problems are meaningful in the context of quantum
information. This work describes Seidel switching from a quantum perspective.
Here, we generalize Seidel switching to weighted directed graphs. We use it to
construct graphs with equal Laplacian and signless Laplacian spectra and
consider density matrices corresponding to them. Hence Seidel switching is a
technique to generate cospectral density matrices. Next, we show that all the
unitary operators used in Seidel switching are global unitary operators. Global
unitary operators can be used to generate entanglement, a benchmark phenomena
in quantum information processing.
