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arXiv · 1509.07586

An extending result on spectral radius of bipartite graphs

Yen-Jen Cheng·Feng-lei Fan·Chih-wen Weng
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Abstract

Let $G$ denote a bipartite graph with $e$ edges without isolated vertices. It was known that the spectral radius of $G$ is at most the square root of $e$, and the upper bound is attained if and only if $G$ is a complete bipartite graph. Suppose that $G$ is not a complete bipartite graph, and $e-1$ and $e+1$ are not twin primes. We determine the maximal spectral radius of $G$. As a byproduct of our study, we obtain a spectral characterization of a pair $(e-1, e+1)$ of integers to be a pair of twin primes.

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Yen-Jen Cheng, Feng-lei Fan, Chih-wen Weng. 2015-11-04. An extending result on spectral radius of bipartite graphs. https://arxiv.org/abs/1509.07586

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