On graph entropy measures based on the number of independent sets and matchings

被引：10

作者：

Wan, Pengfei ^{[1
,2
]}

Chen, Xinzhuang ^{[2
]}

Tu, Jianhua ^{[3
]}

Dehmer, Matthias ^{[4
,5
,6
]}

Zhang, Shenggui ^{[2
]}

Emmert-Strei, Frank ^{[7
,8
]}

机构：

[1] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China

[2] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China

[3] Beijing Univ Chem Technol, Dept Math, Beijing 100029, Peoples R China

[4] Nankai Univ, Coll Comp & Control Engn, Tianjin 300071, Peoples R China

[5] UMIT, Dept Biomed Comp Sci & Mech, Eduard Wallnoefer Zentrum 1, A-6060 Hall In Tirol, Austria

[6] Univ Appl Sci Upper Austria, Fac Management, Prod & Operat Management, Wehrgrabengasse 1-3, A-4400 Steyr, Austria

[7] Tampere Univ, Fac Informat Technol & Commun Sci, Predict Soc & Data Analyt Lab, Tampere, Finland

[8] Inst Biosci & Med Technol, Tampere, Finland

来源：

INFORMATION SCIENCES | 2020年 / 516卷 / 516期

基金：

中国国家自然科学基金;

关键词：

Graph entropy measures; Subgraph; Independent set; Matching; Quantitative graph theory; EXTREMAL PROPERTIES; INEQUALITIES; INDEX; COMPLEXITY; NETWORKS;

D O I：

10.1016/j.ins.2019.11.020

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider the graph entropy measures based on the number of independent sets and matchings. The reason to study these measures relates to the fact that the independent set and matching problem is computationally demanding. However, these features can be calculated for smaller networks. In case one can establish efficient estimations, those measures may be also used for larger graphs. So, we establish some upper and lower bounds as well as some information inequalities for these information-theoretic quantities. In order to give further evidence, we also generate numerical results to study these measures such as list the extremal graphs for these entropies. Those results reveal the two entropies possess some new features. (C) 2019 Published by Elsevier Inc.

引用

页码：491 / 504

页数：14

共 50 条

[1] Problems on matchings and independent sets of a graph
Bhattacharya, Amitava
Mondal, Anupam
Murthy, T. Srinivasa
DISCRETE MATHEMATICS, 2018, 341 (06) : 1561 - 1572
[2] A note on the number of matchings and independent sets in trees
Fischermann, M
Volkmann, L
Rautenbach, D
DISCRETE APPLIED MATHEMATICS, 2005, 145 (03) : 483 - 489
[3] Coverings, matchings and the number of maximal independent sets of graphs
Do Trong Hoang
Tran Nam Trung
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2019, 73 : 424 - 431
[4] On the number of maximal independent sets in a graph
Wood, David R.
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2011, 13 (03): : 17 - 19
[5] The number of independent sets in an irregular graph
Sah, Ashwin
Sawhney, Mehtaab
Stoner, David
Zhao, Yufei
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2019, 138 : 172 - 195
[6] The number of independent sets in a grid graph
Calkin, NJ
Wilf, HS
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1998, 11 (01) : 54 - 60
[7] The Number of Independent Sets in a Regular Graph
Zhao, Yufei
COMBINATORICS PROBABILITY & COMPUTING, 2010, 19 (02): : 315 - 320
[8] On the Number of Matchings and Independent Sets in (3,6)-Fullerenes
Behmaram, A.
Yousefi-Azari, H.
Ashrafi, A. R.
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2013, 70 (02) : 525 - 532
[9] Network Entropies Based on Independent Sets and Matchings
Cao, Shujuan
Dehmer, Matthias
Kang, Zhe
APPLIED MATHEMATICS AND COMPUTATION, 2017, 307 : 265 - 270
[10] THE NUMBER OF MAXIMAL INDEPENDENT SETS IN A CONNECTED GRAPH
GRIGGS, JR
GRINSTEAD, CM
GUICHARD, DR
DISCRETE MATHEMATICS, 1988, 68 (2-3) : 211 - 220

← 1 2 3 4 5 →