The effect of graph operations on the degree-based entropy

Yanni Dong; Hajo Broersma; Changwu Song; Pengfei Wan; Shenggui Zhang

doi:10.1016/j.amc.2022.127533

The effect of graph operations on the degree-based entropy

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

数学与统计学院

Northwestern Polytechnical University Xian
University of Twente
Delft University of Technology
Yulin University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

The degree-based entropy I_d(G) of a graph G on m>0 edges is obtained from the well-known Shannon entropy −∑_i=1ⁿp(x_i)logp(x_i) in information theory by replacing the probabilities p(x_i) by the fractions [Formula presented], where {v₁,v₂,…,v_n} is the vertex set of G, and d_G(v_i) is the degree of v_i. We continue earlier work on I_d(G). Our main results deal with the effect of a number of graph operations on the value of I_d(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.

源语言	英语
文章编号	127533
期刊	Applied Mathematics and Computation
卷	437
DOI	https://doi.org/10.1016/j.amc.2022.127533
出版状态	已出版 - 15 1月 2023

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title = "The effect of graph operations on the degree-based entropy",

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 [Formula presented], 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 = "Degree, Graph entropy, Graph operation, Tree, Unicyclic graph",

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

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day = "15",

doi = "10.1016/j.amc.2022.127533",

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T1 - The effect of graph operations on the degree-based entropy

AU - Dong, Yanni

AU - Broersma, Hajo

AU - Song, Changwu

AU - Wan, Pengfei

AU - Zhang, Shenggui

PY - 2023/1/15

Y1 - 2023/1/15

N2 - 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 [Formula presented], 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.

AB - 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 [Formula presented], 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.

KW - Degree

KW - Graph entropy

KW - Graph operation

KW - Tree

KW - Unicyclic graph

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DO - 10.1016/j.amc.2022.127533

M3 - 文章

AN - SCOPUS:85138046817

SN - 0096-3003

VL - 437

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 127533

ER -

The effect of graph operations on the degree-based entropy

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