collaborators

6 papers

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

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…

math.CO2025

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…

math.CO2025

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} |…

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…

math.CO2024

A Linear Lower Bound for the Square Energy of Graphs

Saieed Akbari, Hitesh Kumar, Bojan Mohar +1

Let be a graph of order with eigenvalues . Let \[s^+(G)=\sum_{λ_i>0} λ_i^2, \qquad s^-(G)=\sum_{λ_i<0} λ_i^2.\] The smaller value, $s(G)=\min\{s^+(…