3 papers
math.CO2025
Spectrally symmetric orientations of graphs
Saieed Akbari, Jonathan Aloni, Maxwell Levit +2
The Hermitian adjacency matrices of digraphs based on the sixth root of unity were introduced in [B. Mohar, A new kind of Hermitian matrices for digraphs, Linear Alg. Appl. (2020)]…
math.CO2025
Tight Bounds for Cycle-Edge Decompositions and Covers
Saieed Akbari, Jonny Aloni, Arash Beikmohammadi +1
An old conjecture of Erd{ő}s and Gallai states that every vertex graph can be decomposed, that is can be partitioned, into cycles and edges. The covering version…
math.CO2025
Hermitian adjacency matrices with at most three distinct eigenvalues
Saieed Akbari, Jonathan Aloni, Maxwell Levit +2
We study oriented graphs whose Hermitian adjacency matrices of the second kind have few eigenvalues. We give a complete characterization of the oriented graphs with two distinct ei…