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arXiv · 2503.17883

On the maximum spectral radius of connected graphs with a prescribed order and size

Ivan Damnjanović
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Abstract

The spectral radius of a graph is the largest modulus of an eigenvalue of its adjacency matrix. Let $\mathcal{C}_{n, e}$ be the set of all the connected simple graphs with $n$ vertices and $n - 1 + e$ edges. Here, we solve the spectral radius maximization problem on $\mathcal{C}_{n, e}$ when $e \le 130$ or $n \ge e + 2 + 13\sqrt{e}$.

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Ivan Damnjanović. 2025-04-03. On the maximum spectral radius of connected graphs with a prescribed order and size. https://arxiv.org/abs/2503.17883

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