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

^*Corresponding author for this work

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

2 Citations (Scopus)

176 Downloads (Pure)

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
Publication status	Published - 15 Jan 2023

Keywords

Degree
Graph entropy
Graph operation
Tree
Unicyclic graph
UT-Hybrid-D

Access to Document

10.1016/j.amc.2022.127533Licence: CC BY

ArticleFinal published version, 900 KBLicence: CC BY

Cite this

@article{2efc596d2f1642a0aba046d2cf583bbf,

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, UT-Hybrid-D",

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

note = "Funding Information: This research was supported by the National Natural Science Foundation of China (Nos. 12071370 , 12131013 and U1803263 ) and the China Scholarship Council (No. 202006290070 ). Publisher Copyright: {\textcopyright} 2022",

year = "2023",

month = jan,

day = "15",

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

language = "English",

volume = "437",

journal = "Applied mathematics and computation",

issn = "0096-3003",

publisher = "Elsevier",

}

TY - JOUR

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

N1 - Funding Information: This research was supported by the National Natural Science Foundation of China (Nos. 12071370 , 12131013 and U1803263 ) and the China Scholarship Council (No. 202006290070 ). Publisher Copyright: © 2022

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

KW - UT-Hybrid-D

UR - https://www.scopus.com/pages/publications/85138046817

U2 - 10.1016/j.amc.2022.127533

DO - 10.1016/j.amc.2022.127533

M3 - Article

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this