Speaker: Muhammad Irfan Arsyad Prayitno
Topic: Adjacency and Hermitian Adjacency of Mixed Graphs
Date: Wednesday, May 20, 2026
Time: 09.00 – 10.00 AM
Venue: Room 320 (Master’s/Doctoral Program in Mathematics), Building F, 3rd Floor
The Mathematics PhD Students Colloquium continued by Muhammad Irfan Arsyad Prayitno from our algebra laboratory on the topic “Adjacency and Hermitian Adjacency of Mixed Graphs.”
He began the talk by introducing several types of graphs, namely undirected graphs, directed graphs (digraphs), and mixed graphs, highlighting the differences between these structures. He then presented the adjacency matrix and several versions of the Hermitian adjacency matrix associated with mixed graphs, explaining how these matrices can be used to study graph properties through linear algebraic methods.
To support the discussion, Irfan demonstrated a Python program that computes important spectral characteristics of these matrices, including determinants, eigenvalues, and characteristic polynomials. This computational approach illustrated how spectral information can be obtained efficiently and used to investigate graph structures.
During the discussion session, participants raised questions regarding graphs that share identical spectral properties. In response, Irfan introduced the notion of cospectral graphs, namely distinct graphs whose associated matrices have the same spectrum. Another discussion focused on potential applications of studying the spectral properties of complement graphs, complement digraphs, and complement mixed graphs. While these applications remain part of his ongoing investigation, he emphasized that understanding the fundamental properties of adjacency and Hermitian adjacency matrices is an important first step toward exploring broader applications.
