2 research outputs found
Symmetry in complex unit gain graphs and their spectra
Complex unit gain graphs may exhibit various kinds of symmetry. In this work,
we explore structural symmetry, spectral symmetry and sign-symmetry in gain
graphs, and their respective relations to one-another. Our main result is a
construction that transforms an arbitrary gain graph into infinitely many
switching-distinct gain graphs whose spectral symmetry does not imply
sign-symmetry. This provides a more general answer to the gain graph analogue
of an existence question that was recently treated in the context of signed
graphs