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arXiv · 1509.07372

On the spectral radius of simple digraphs with prescribed number of arcs

Ya-Lei Jin·Xiao-Dong Zhang
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Abstract

This paper presents a sharp upper bound for the spectral radius of simple digraphs with described number of arcs. Further, the extremal graphs which attain the maximum spectral radius among all simple digraphs with fixed arcs are investigated. In particular, we characterize all extremal simple digraphs with the maximum spectral radius among all simple digraphs with arcs number $e=2{k\choose 2}+t$ and $k>4t^4+4$.

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Ya-Lei Jin, Xiao-Dong Zhang. 2015-09-24. On the spectral radius of simple digraphs with prescribed number of arcs. https://arxiv.org/abs/1509.07372

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