S. Akbari

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20242026

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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…