[1]刘胜久,伍小兵,曹小平,等.有向超图的超网络能量及其性质[J].南京师范大学学报(工程技术版),2022,22(04):036-44.[doi:10.3969/j.issn.1672-1292.2022.04.005]
　Liu Shengjiu,Wu Xiaobing,Cao Xiaoping,et al.Hypernetwork Energy of Directed Hypergraphs and Its Properties[J].Journal of Nanjing Normal University(Engineering and Technology),2022,22(04):036-44.[doi:10.3969/j.issn.1672-1292.2022.04.005]
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有向超图的超网络能量及其性质
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南京师范大学学报（工程技术版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
22卷
期数:
2022年04期
页码:
036-44
栏目:
计算机科学与技术
出版日期:
2022-12-15

文章信息/Info

Title:
Hypernetwork Energy of Directed Hypergraphs and Its Properties
文章编号:
1672-1292(2022)04-0036-09
作者:
刘胜久1; 伍小兵1; 曹小平2; 汪应1; 欧明辉1
(1.重庆工程职业技术学院大数据与物联网学院,重庆 402260)
(2.重庆科创职业学院人工智能学院,重庆 402160)
Author(s):
Liu Shengjiu1; Wu Xiaobing1; Cao Xiaoping2; Wang Ying1; Ou Minghui1
(1.Big Data and Internet of Things School,Chongqing Vocational Institute of Engineering,Chongqing 402260,China)
(2.School of Artical Intelligence,Chongqing Creation Vocational College,Chongqing 402160,China)
关键词:
复杂网络; 超图; 有向超图; 图能量; 网络能量; 超网络能量
Keywords:
complex network; hypergraph; directed hypergraph; graph energy; network energy; hypernetwork energy
分类号:
TP391
DOI:
10.3969/j.issn.1672-1292.2022.04.005
文献标志码:
A
摘要:
图能量表述为方阵形式的矩阵特征值绝对值之和. 网络能量已在无向图、有向图及混合图中得到较为成功的应用,与传统意义上的图能量之间存在多个相同或相似的上下限. 由于图与超图之间的关联,无向图与有向图的网络能量及无向超图的超网络能量之间存在密切联系. 将超网络能量由无向超图推广应用到有向超图,提出了有向超图的超网络能量,分析了无向超图与有向超图的超网络能量之间的关联,同时论述了无向图与有向图的网络能量及无向超图与有向超图的超网络能量之间的联系,最后给出了有向超图的超网络能量若干重要性质.
Abstract:
Graph energy is expressed as the sum of all absolute values of eigenvalues of square matrix. Network energies have been applied in undirected graphs,oriented graphs,and mixed graphs successfully,and share several same or similar lower bounds or upper bounds with traditional graph energies. For the relationship between graph and hypergraph,there are closely relationships among network energies of undirected graph and oriented graph and hypernetwork energy of undirected hypergraph. In this paper,the hypernetwork energy of directed hypergraphs is proposed by extended hypernetwork energy from undirected hypergraph to directed hypergraph. The relationship between hypernetwork energies of undirected hypergraph and directed hypergraph is analyzed,and the relationships among network energy of undirected graph and oriented graph and hypernetwork energies of undirected hypergraph and directed hypergraph are also discussed. Finally,several important properties of hypernetwork energy of directed hypergraph are analyzed as well.

参考文献/References:

[1]GUTMAN I. The energy of graph[J]. Ber Math Statist Sekt Forsch Graz,1978,22(103):2179-2187.
[2]DEWAR M J S. The molecular orbital theory of organic chemistry[M]. New York:McGraw-Hill,1969.
[3]ADIGA C,BALAKRISHNAN R,SO W. The skew energy of a digraph[J]. Linear Algebra and Its Applications,2010,432(7):1825-1835.
[4]GUTMAN I,FURTULA B. Survey of graph energies[J]. Mathematics Interdisciplinary Research,2017,2:85-129.
[5]INDULAL G,GUTMAN I,VIJAYAKUMAR A. On distance energy of graphs[J]. Communications in Mathematical and in Computer Chemistry,2008,60(2):461-472.
[6]LIU J P,LIU B L. A Laplacian-energy like invariant of a graph[J]. Communications in Mathematical and in Computer Chemistry,2008,59(2):355-372.
[7]JOOYANDEH M,KIANI D,MIRZAKHAH M. Incidence energy of a graph[J]. Communications in Mathematical and in Computer Chemistry,2009,62(3):561-572.
[8]GUTMAN I,WAGNER S. The matching energy of a graph[J]. Discrete Applied Mathematics,2012,160(15):2177-2187.
[9]GUTMAN I,ZHOU B. Laplacian energy of a graph[J]. Linear Algebra and Its Applications,2006,414(1):29-37.
[10]SO W,ROBBIANO M,ABREU N D. Applications of a theorem by Ky Fan in the theory of graph energy[J]. Linear Algebra and its Applications,2010,432(9):2163-2169.
[11]BRYC W,DEMBO A,JIANG T. Spectral measure of large random Hankel,Markov and Toeplitz matrices[J]. The Annals of Probability,2006,34(1):1-38.
[12]DASA K,AOUCHICHE M,HANSEN P. On(distance)Laplacian energy and(distance)signless Laplacian energy of graphs[J]. Discrete Applied Mathematics,2018,243:172-185.
[13]唐保祥,任韩. 3类图完美匹配的计数[J]. 南京师大学报(自然科学版),2012,35(1):16-21.
[14]赵春红,董伟. 平面图3可着色的充分条件[J]. 南京师大学报(自然科学版),2011,34(9):13-18.
[15]秦荪榛,凌秀泽,徐寅林. 基于无线传感网络的血氧实时监测系统的研究与设计[J]. 南京师范大学学报(工程技术版),2012,12(4):39-43.
[16]凌秀泽,秦荪榛,徐寅林. 心电信号无线传输网络节点的研究与实现[J]. 南京师范大学学报(工程技术版),2012,12(3):71-75.
[17]刘胜久,李天瑞,刘小伟. 网络维数:一种度量复杂网络的新方法[J]. 计算机科学,2019,46(1):51-56.
[18]LIU S J,LI T R,ZHU J,et al. Network energy:A new energy of a graph[C]//Proceedings of 2019 IEEE 14th International Conference on Intelligent Systems and Knowledge Engineering. Dalian,China,2019:785-789.
[19]LIU S J,LI T R,ZHANG X B,et al. On network energy of oriented graphs[C]//Proceedings of the 14th International FLINS Conference on Robotics and Artificial Intelligence. Cologne,Germany,2020:11-18.
[20]刘胜久,李天瑞,谢鹏,等. 网络能量在混合图中的研究与应用[J]. 湖南大学学报(自然科学版),2021,48(6):105-111.
[21]刘胜久,李天瑞,杨宗霖,等. 带权超网络的度量方法及其性质[J]. 计算机应用,2019,39(11):3107-3113.
[22]刘胜久,李天瑞,刘佳,等. 超网络能量研究与应用[J]. 计算机科学与探索,2021,15(4):682-689.
[23]王建方. 超图的理论基础[M]. 北京:高等教育出版社,2006.
[24]GALLO G,LONGO G,PALLOTTINO S,et al. Directed hypergraphs and applications[J]. Discrete Applied Mathematics,1993,42:177-201.
[25]FENG K Q,LI W W. Spectra of hypergraphs and applications[J]. Journal of Number Theory,1996,60(1):1-22.
[26]刘胜久,李天瑞,洪西进,等. 超网络模型构建及特性分析[J]. 计算机科学与探索,2017,11(2):194-211.

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备注/Memo

备注/Memo:
收稿日期:2022-03-16.
基金项目:重庆市高校创新研究群体项目(CXQT21032)、重庆市自然科学基金项目(cstc2021jcyj-msxmX0532)、重庆市教育委员会科学技术研究计划项目(KJQN202103404、KJQN202005403、KJQN202003409、KJQN202103401、KJZD-M202203401)、重庆市高等教育教学改革研究重点项目(202182)、重庆市高等职业教育教育改革研究项目(Z212026).
通讯作者:刘胜久,博士,研究方向:复杂网络、自然语言处理和大数据. E-mail:liushengjiu2008@163.com
更新日期/Last Update: 2022-12-15