Resolution of Yan's conjecture on entropy of graphs

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.

11 pages, 1 table (containing 5 figures)