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Symmetry in complex unit gain graphs and their spectra
Pepijn Wissing, Edwin R. van Dam
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 respecti…
Self-converse mixed graphs are extremely rare
Pepijn Wissing
A mixed graph is cospectral to its converse, with respect to the usual adjacency matrices. Hence, it is easy to see that a mixed graph whose eigenvalues occur uniquely, up to isomo…
Unit gain graphs with two distinct eigenvalue and systems of lines in complex space
Pepijn Wissing, Edwin R. van Dam
Since the introduction of the Hermitian adjacency matrix for digraphs, interest in so-called complex unit gain graphs has surged. In this work, we consider gain graphs whose spectr…
Spectral Fundamentals and Characterizations of Signed Directed Graphs
Pepijn Wissing, Edwin R. van Dam
The spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention…
The negative tetrahedron and the first infinite family of connected digraphs that are strongly determined by the Hermitian spectrum
Pepijn Wissing, Edwin R. van Dam
Thus far, digraphs that are uniquely determined by their Hermitian spectra have proven elusive. Instead, researchers have turned to spectral determination of classes of switching e…