The effect of graph operations on the degree-based entropy

Yanni Dong, Hajo Broersma, Changwu Song, Pengfei Wan and Shenggui Zhang

Applied Mathematics and Computation, 2023, vol. 437, issue C

Abstract: The degree-based entropy Id(G) of a graph G on m>0 edges is obtained from the well-known Shannon entropy −∑i=1np(xi)logp(xi) in information theory by replacing the probabilities p(xi) by the fractions dG(vi)2m, where {v1,v2,…,vn} is the vertex set of G, and dG(vi) is the degree of vi. We continue earlier work on Id(G). Our main results deal with the effect of a number of graph operations on the value of Id(G). We also illustrate the relevance of these results by applying some of these operations to prove a number of extremal results for the degree-based entropy of trees and unicyclic graphs.

Keywords: Graph entropy; Graph operation; Degree; Tree; Unicyclic graph (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:437:y:2023:i:c:s0096300322006075

DOI: 10.1016/j.amc.2022.127533

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