Hitesh Kumar

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20242026

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11 papers · 1 filter

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

Resolution of a problem of Mohar on non-positive inertia

Clive Elphick, Hitesh Kumar, Shivaramakrishna Pragada +1

For a graph $G$ of order $n$ , its positive, negative and non-positive inertia is the number of positive, negative and non-positive eigenvalues of its adjacency matrix $A (G)$ , respe…

math.FA2026

Stability of maximal relative projection constants

Hitesh Kumar, Bojan Mohar, Seyed Ahmad Mojallal +1

For positive integers $n \geq r$ , let $λ (r, n)$ denote the \emph{maximal relative projection constant} of $r$ -dimensional subspaces of $ℓ_{\infty}^{n}$ and $λ (r)$ denote the \emph{maxi…

math.CO2026

Localization of the Caro-Wei bound and its applications to bipartiteness

Aida Abiad, Hitesh Kumar, Shivaramakrishna Pragada

We confirm a conjecture of Brause, Randerath, Rautenbach and Schiermeyer (2016) by proving a localized lower bound on the independence number of a graph that strengthens the classi…

math.CO2026

A proof of the cyclotomic conjecture and the non-existence of almost Moore digraphs

Jaskaran Kaur, Hitesh Kumar

For $n > 2$ and $k > 1$ , define the polynomial \[F_{n,k}(x) = Φ_n(1 + x + \cdots + x^k),\] where $Φ_{n}$ denotes the $n$ -th cyclotomic polynomial. The \emph{cyclotomic conjecture} propos…

math.CO2026

Extremal graphs for the $k$ -th eigenvalue

Hitesh Kumar, Bojan Mohar, Seyed Ahmad Mojallal +1

For a simple graph $G$ of order $n$ , let $λ_{1} (G) \geq \dots \geq λ_{n} (G)$ denote its adjacency eigenvalues. Hong's problem asks for the optimal upper bound for $λ_{k} (G)$ . A recent theo…

math.CO2026

Energy and independence number

Hitesh Kumar, Shivaramakrishna Pragada

For a graph $G$ of order $n$ , with adjacency eigenvalues $λ_{1} (G) \geq \dots \geq λ_{n} (G)$ , the \emph{energy} of $G$ is defined to be \[\mathcal{E}(G)=\sum_{i=1}^{n} |λ_i(G)|.\] A w…

math.CO2026

An improved bound for the strong clique index of graphs

Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada

For a graph $G$ with line graph $L (G)$ , $χ (L (G)^{2})$ and $ω (L (G)^{2})$ are called the \emph{strong chromatic index} and \emph{strong clique index} of $G$ , respectively. A well-known c…

math.CO2026

Localized Turán-type inequalities for $Q$ -index

M. Rajesh Kannan, Hitesh Kumar, Shivaramakrishna Pragada

For a connected graph $G$, let $q (G)$ denote the $Q$ -index of $G$ , i.e., the largest eigenvalue of its signless Laplacian matrix. Abreu and Nikiforov (2013) showed that \[ q(G) \…

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.CO2026

Convex combination of first and second eigenvalues of trees

Hitesh Kumar, Bojan Mohar, Shivaramakrishna Pragada +1

For a graph $G$ , let $λ_{1} (G)$ and $λ_{2} (G)$ denote the largest and the second largest adjacency eigenvalue of $G$ . The sum $λ_{1} (G) + λ_{2} (G)$ is called the \emph{spectral sum} of $G$ …

The switching conjecture for main eigenvalues is asymptotically true

Resolution of a problem of Mohar on non-positive inertia

Stability of maximal relative projection constants

Localization of the Caro-Wei bound and its applications to bipartiteness

A proof of the cyclotomic conjecture and the non-existence of almost Moore digraphs

Extremal graphs for the k-th eigenvalue

Energy and independence number

An improved bound for the strong clique index of graphs

Localized Turán-type inequalities for Q-index

Maximum spectral sum of graphs

Convex combination of first and second eigenvalues of trees

Extremal graphs for the $k$ -th eigenvalue

Localized Turán-type inequalities for $Q$ -index