Minimum entropy of graphs with given size

The first degree-based graph entropy of a graph is the Shannon entropy of its degree sequence. Its correct interpretation as a measure of uniformity of the degree sequence requires the determination of its extremal values given natural constraints. In this paper, we prove that the graphs with given size that minimize the first degree-based graph entropy are precisely the colex graphs.

Authors

Stijn Cambie (ORCID: https://orcid.org/0000-0002-2385-1137)
Matteo Mazzamurro (ORCID: https://orcid.org/0009-0004-4454-1551)

Institutions

Queen Mary University of London (GB)
Vlakwa (BE)

Publication Details

Journal: Discrete Mathematical Chemistry
Published: 2025-09-24
DOI: https://doi.org/10.26493/2820-6657.3.bfd
Citations: 1
Primary Topic: Graph theory and applications
Type: article
Field-Weighted Citation Impact: 0.00

Funders

University of Warwick
Engineering and Physical Sciences Research Council

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article

Minimum entropy of graphs with given size

Stijn Cambie, Matteo Mazzamurro

Sep 24, 2025

1 citations

Discrete Mathematical Chemistry

Graph theory and applications

article

Minimum entropy of graphs with given size

Stijn Cambie, Matteo Mazzamurro

September 24, 2025article en

1 citations

Abstract

The first degree-based graph entropy of a graph is the Shannon entropy of its degree sequence. Its correct interpretation as a measure of uniformity of the degree sequence requires the determination of its extremal values given natural constraints. In this paper, we prove that the graphs with given size that minimize the first degree-based graph entropy are precisely the colex graphs.

Discrete Mathematical ChemistryVol. 25(1)

Queen Mary University of London (GB), Vlakwa (BE)

University of Warwick, Engineering and Physical Sciences Research Council

Openalex Percentile: Top 99%

Graph theory and applications

DOI Open Access PDF OpenAlex

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Minimum entropy of graphs with given size — Stijn Cambie, Matteo Mazzamurro · Discrete Mathematical Chemistry (2025) | TGRS Research Map | TGRS