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

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Article number	127533
Journal	Applied Mathematics and Computation
Volume	437
DOIs	https://doi.org/10.1016/j.amc.2022.127533
State	Published - 15 Jan 2023

Keywords

Degree
Graph entropy
Graph operation
Tree
Unicyclic graph

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10.1016/j.amc.2022.127533

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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.",

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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

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JO - Applied Mathematics and Computation

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The effect of graph operations on the degree-based entropy

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Keywords

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