S. Akbari

activity

20242026

collaborators

12 papers

math.CO2026

The switching conjecture for main eigenvalues is asymptotically true

Saieed Akbari, Hitesh Kumar, Bojan Mohar +1

An eigenvalue of a signed graph is called \emph{main} if there exists a corresponding eigenvector non-orthogonal to the all-ones vector. An important result of O'Rourke and Touri (…

math.CO2026

Bounds for the Vertex Chromatic Number of Connected Triangle-Free Graphs

Saieed Akbari, Arash Beikmohammadi

It was recently shown that every connected graph of order $n \geq 5$ and size $m$ satisfies $χ (G) \leq ⌈ \frac{m}{n} ⌉$ , and it was asked whether the st…

math.CO2026

Distribution of signless Laplacian eigenvalues and degree sequence

Saieed Akbari, M. Darougheh, L. S. de Lima +1

Let $G$ be a graph of order $n$ with degree sequence $d_{1} \geq \dots \geq d_{n}$ . Let $m_{G} I$ be the number of signless Laplacian eigenvalues in an interval $I$ . In this paper, w…

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 $n$ vertex graph can be decomposed, that is $E (G)$ can be partitioned, into $O (n)$ cycles and edges. The covering version…

math.CO2025

A new conjecture on the inertia of graphs

Saieed Akbari, Clive Elphick, Hitesh Kumar +2

Let $G$ be a graph with adjacency matrix $A (G)$ . We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where $n^{+} (G)$ and $n^{-} (G)$ 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 $G$ be a simple graph of order $n$ with eigenvalues $λ_{1} (G) \geq \dots \geq λ_{n} (G)$ . 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 $p$ -Energy of Graphs

Saieed Akbari, Hitesh Kumar, Bojan Mohar +1

For a Hermitian matrix $A$ of order $n$ with eigenvalues $λ_{1} (A) \geq \dots \geq λ_{n} (A)$ , 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 $G$ be a graph of order $n$ with eigenvalues $λ_{1} \geq \dots \geq λ_{n}$ . 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^+(…

math.CO2024

Line graphs and Nordhaus-Gaddum-type bounds for self-loop graphs

Saieed Akbari, Irena M. Jovanović, Johnny Lim

Let $G_{S}$ be the graph obtained by attaching a self-loop at every vertex in $S \subseteq V (G)$ of a simple graph $G$ of order $n .$ In this paper, we explore several new results rel…

math.CO2024

On the $Δ$ -edge stability number of graphs

Saieed Akbari, Reza Hosseini Dolatabadi, Mohsen Jamaali +2

The $Δ$ -edge stability number $es_{Δ} (G)$ of a graph $G$ is the minimum number of edges of $G$ whose removal results in a subgraph $H$ with $Δ (H) = Δ (G) - 1$ . Sets whose removal…

The switching conjecture for main eigenvalues is asymptotically true

Bounds for the Vertex Chromatic Number of Connected Triangle-Free Graphs

Distribution of signless Laplacian eigenvalues and degree sequence

Spectrally symmetric orientations of graphs

Tight Bounds for Cycle-Edge Decompositions and Covers

A new conjecture on the inertia of graphs

Refinement of a conjecture on positive square energy of graphs

Vertex Partitioning and p-Energy of Graphs

Hermitian adjacency matrices with at most three distinct eigenvalues

A Linear Lower Bound for the Square Energy of Graphs

Line graphs and Nordhaus-Gaddum-type bounds for self-loop graphs

On the Δ-edge stability number of graphs

Vertex Partitioning and $p$ -Energy of Graphs

On the $Δ$ -edge stability number of graphs