Symmetry in complex unit gain graphs and their spectra
Combinatorics
2024-10-04 v2
Abstract
Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a construction that transforms an arbitrary complex unit gain graph into infinitely many switching-distinct ones whose spectral symmetry does not imply sign-symmetry. This provides a more general answer to the analogue of an existence question that was recently treated in the context of signed graphs.
Cite
@article{arxiv.2305.15207,
title = {Symmetry in complex unit gain graphs and their spectra},
author = {Pepijn Wissing and Edwin R. van Dam},
journal= {arXiv preprint arXiv:2305.15207},
year = {2024}
}