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arXiv · 2205.03357

Resolution of Yan's conjecture on entropy of graphs

Stijn Cambie·Matteo Mazzamurro
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Abstract

The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. In this paper, we characterize the connected graphs with given order $n$ and size $m$ that minimize the first degree-based entropy whenever $n-1 \le m \le 2n-3,$ thus extending and proving a conjecture by Yan.

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Stijn Cambie, Matteo Mazzamurro. 2022-05-06. Resolution of Yan's conjecture on entropy of graphs. https://arxiv.org/abs/2205.03357

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