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Graphs with minimum degree-entropy

Dong, Yanni; Gadouleau, Maximilien; Wan, Pengfei; Zhang, Shenggui

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Authors

Yanni Dong

Pengfei Wan

Shenggui Zhang



Abstract

We continue studying extremal values of the degree-entropy, which is an information-theoretic measure defined as the Shannon entropy based on the information functional involving vertex degrees. For a graph with a given number of vertices and edges achieving the minimum entropy value, we show its unique structure. Also, a tight lower bound for the entropy in bipartite graphs with a given number of vertices and edges is proved. Our result directly derives the result of Cao et al. (2014) that for a tree with a given number of vertices, the minimum value of the entropy is attained if and only if the tree is the star.

Citation

Dong, Y., Gadouleau, M., Wan, P., & Zhang, S. (2024). Graphs with minimum degree-entropy. Information Sciences, 671, 120629. https://doi.org/10.1016/j.ins.2024.120629

Journal Article Type Article
Acceptance Date Apr 10, 2024
Online Publication Date Apr 30, 2024
Publication Date 2024-06
Deposit Date Jun 7, 2024
Publicly Available Date Jun 7, 2024
Journal Information Sciences
Print ISSN 0020-0255
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 671
Pages 120629
DOI https://doi.org/10.1016/j.ins.2024.120629
Public URL https://durham-repository.worktribe.com/output/2475188

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