Hitesh Kumar

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20242026

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8 papers · 1 filter

math.CO2026

Maximum spectral sum of graphs

Hitesh Kumar, Lele Liu, Hermie Monterde +2

For a graph $G$ of order $n$ , the spectral sum of $G$ is defined to be the sum $λ_{1} (G) + λ_{2} (G)$ , where $λ_{1} (G)$ (resp. $λ_{2} (G)$ ) is the largest (resp. second largest) adjacency ei…

math.CO2025

Localization of spectral Turán-type theorems

M. Rajesh Kannan, Hitesh Kumar, Shivaramakrishna Pragada

Let $G$ be a graph, and let $v$ and $e$ be a vertex and an edge of $G$ , respectively. Define $c (v)$ (resp. $c (e)$ ) to be the order of the largest clique in $G$ containing $v$ (resp…

math.CO2025

Improved Bounds for the Ultimate Independence Ratio of Odd Wheels

Alexander Clow, Hitesh Kumar, Shivaramakrishna Pragada

The ultimate independence ratio of a graph $G$ is defined as $I (G) = lim_{k \to \infty} \frac{α ( G ^{□ k} )}{∣ V ( G ) ∣ ^{k}},$ where $α (G^{□ k})$ is the independence…

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} |…

Maximum spectral sum of graphs

Localization of spectral Turán-type theorems

Improved Bounds for the Ultimate Independence Ratio of Odd Wheels

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

Vertex Partitioning and $p$ -Energy of Graphs