Resolution of Yan's conjecture on entropy of graphs

Stijn Cambie; Matteo Mazzamurro

Resolution of Yan's conjecture on entropy of graphs

Combinatorics 2022-05-09 v1

Authors: Stijn Cambie , Matteo Mazzamurro

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.

Keywords

graph entropy degree-based entropy connected graphs yan conjecture shannon entropy

Cite

@article{arxiv.2205.03357,
  title  = {Resolution of Yan's conjecture on entropy of graphs},
  author = {Stijn Cambie and Matteo Mazzamurro},
  journal= {arXiv preprint arXiv:2205.03357},
  year   = {2022}
}

Comments

11 pages, 1 table (containing 5 figures)

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