Extremality of Graph Entropy Based on Degrees of Uniform Hypergraphs with Few Edges

Dan Hu, Xue Liang Li, Xiao Gang Liu, Sheng Gui Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Let H be a hypergraph with n vertices. Suppose that d1,d2,…,dn are degrees of the vertices of H. The t-th graph entropy based on degrees ofH is defined as Idt(H)=−∑i=1n(dit∑j=1ndjtlogdit∑j=1ndjt)=log(∑i=1ndit)−∑i=1n(dit∑j=1ndjtlogdit), where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of Idt(H) for t = 1, when H is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.

Original languageEnglish
Pages (from-to)1238-1250
Number of pages13
JournalActa Mathematica Sinica, English Series
Volume35
Issue number7
DOIs
StatePublished - 1 Jul 2019

Keywords

  • degree sequence
  • graph entropy
  • hypergraph
  • Shannon’s entropy

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