27th Conference of the International Linear Algebra Society (ILAS 2026)

Hermitian Spectra of Merged Subdivision Mixed Graphs

May 21, 2026, 2:25 PM

25m

Goodwin Hall 135 (Virginia Tech)

Minisymposium Talk Combinatorial Matrix Theory Combinatorial Matrix Theory

Speaker

Enide Andrade (Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Portugal)

Description

Let $G$ be a mixed graph and let $(H_1, H_2)$ be an ordered pair of mixed graphs whose orders coincide with the order and size of $G$, respectively. We introduce the subdivision mixed graph $S(G)$ and the $(H_1,H_2)$-merged subdivision mixed graph. We investigate the Hermitian spectrum and the Hermitian energy of these graphs, deriving spectral properties that relate merged subdivision mixed graphs to their underlying mixed and undirected counterparts. In particular, we compare the Hermitian energies of certain classes of mixed graphs with those of their underlying graphs, illustrating how the merging process influences spectral behavior. These results show how graph operations influence Hermitian spectral invariants in mixed graphs.
This is joint work with G. Infante, M. Robbiano, Universidad Católica del Norte, Chile,and Eber Lenes, Universidad del Sinú, Colombia