6 papers · 1 filter
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)]…
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…
A new conjecture on the inertia of graphs
Saieed Akbari, Clive Elphick, Hitesh Kumar +2
Let be a graph with adjacency matrix . We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where and denote the number of positive and negative eigen…
Refinement of a conjecture on positive square energy of graphs
Saieed Akbari, Hitesh Kumar, Bojan Mohar +2
Let be a simple graph of order with eigenvalues . Define \[s^+(G)=\sum_{λ_i >0} λ_i^2(G), \quad s^-(G)=\sum_{λ_i<0} λ_i^2(G).\] It was conjec…
Vertex Partitioning and -Energy of Graphs
Saieed Akbari, Hitesh Kumar, Bojan Mohar +1
For a Hermitian matrix of order with eigenvalues , define \[ \mathcal{E}_p^+(A)=\sum_{λ_i > 0} λ_i^p(A), \quad \mathcal{E}_p^-(A)=\sum_{λ_i<0} |…
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…