Topic: Hermitian Adjacency Matrix of Digraphs, Mixed Graph, and Undirected Graphs
Speaker: Muhammad Irfan Arsyad Prayitno
Time: 10:30–11:30 a.m., Wednesday, 18 February 2026
Our PhD student Muhammad Irfan Arsyad Prayitno began his presentation by introducing the antiadjacency matrix of a digraph and explaining its role as an alternative matrix representation in spectral analysis. He discussed results on cyclic digraphs, particularly the directed cyclic sun graph, where he derived explicit forms of the characteristic polynomial and described the corresponding eigenvalue patterns. The presentation emphasized how these graphs exhibit structured and predictable spectral behavior.
He then compared the antiadjacency matrix with other matrix representations of directed cyclic sun graphs, namely, the adjacency matrix, the in-degree Laplacian matrix, and the out-degree Laplacian matrix. For each matrix, he presented formulas for the characteristic polynomial and analyzed the eigenvalue distributions, highlighting similarities and differences in their spectral structures.
The seminar continued with a discussion of generalizations to broader classes of digraphs, including digraphs that allow directed digons and loops. He introduced the concept of powering matrices and examined how powering affects the characteristic polynomial and eigenvalues of the antiadjacency matrix.
Finally, he discussed the spectral properties of iterated line digraphs, explaining how the antiadjacency matrix behaves under this graph operation and presenting results on the corresponding characteristic polynomials and eigenvalues.