Rahul Roy

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20232026

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math.CO2026

A Vertex-Localized Positive Square-Energy Strengthening of Turán's Theorem

Abhay Jayarajan, M. Rajesh Kannan, Shivaramakrishna Pragada +1

Let $G$ be a graph of order $n$ with the adjacency eigenvalues $λ_{1} (G) \geq \dots \geq λ_{n} (G)$ . Let $c (v)$ denote the maximum order of a clique containing vertex $v$ . We prove the…

math.CO2026

Maximizing the algebraic connectivity of graphs of given order and size: a proof of a conjecture of Kolokolnikov

Sebastian M. Cioabă, Abhay Jayarajan, M. Rajesh Kannan +1

The algebraic connectivity of a graph $G$ is a well-studied graph invariant that is related to other properties of the graph such as connectivity and expansion. Given $n$ and $m$ ,…

math.CO2026

Structural and extremal properties of $l_{1}$ -Fiedler value

M. Rajesh Kannan, Rahul Roy

The algebraic connectivity $a (G)$ , defined as the second smallest eigenvalue of the Laplacian matrix $L (G)$ , admits a well-known variational characterization involving the minimiza…

A Vertex-Localized Positive Square-Energy Strengthening of Turán's Theorem

Maximizing the algebraic connectivity of graphs of given order and size: a proof of a conjecture of Kolokolnikov

Structural and extremal properties of l1​-Fiedler value

Structural and extremal properties of $l_{1}$ -Fiedler value