基于拉普拉斯度的k-均匀超图的图熵极值

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (3): 150-155.

基于拉普拉斯度的k-均匀超图的图熵极值

卢鹏丽^*, 薛玉龙

兰州理工大学计算机与通信学院, 甘肃兰州 730050

收稿日期:2019-12-19 出版日期:2021-06-28 发布日期:2021-07-19
通讯作者: 卢鹏丽(1973-),女,甘肃酒泉人,博士,教授,博导.Emial:lupengli88@163.com
基金资助:
国家自然科学基金(11361033)

Extremality of graph entropy based on Laplacian degrees of k-uniform hypergraphs

LU Peng-li, XUE Yu-long

College of Computer and Communication, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2019-12-19 Online:2021-06-28 Published:2021-07-19

摘要/Abstract

摘要： 基于一般图中图熵的定义,定义了超图基于拉普拉斯度的图熵.将简单图的图熵的一些结论推广到k-均匀超图.利用一种移边操作,分别确定了在k-均匀超树、单圈k-均匀超图、双圈k-均匀超图和k-均匀化学超树中基于拉普拉斯度的图熵最大值和最小值,并确定了相应的极值图.

关键词: 图熵, 超图, 拉普拉斯度

Abstract: Motivated by the definition of graph entropy in general graphs, the graph entropy of hypergraphs based on Laplacian degree are defined. Some results on graph entropy of simple graphs are extended to k-uniform hypergraphs. By an operation of edge moving, the maximum and minimum graph entropy based on Laplacian degrees are determined in k-uniform hypertrees, unicyclic k-uniform hypergraphs, bicyclic k-uniform hypergraphs and k-uniform chemical hypertrees, respectively, and the corresponding extremal graphs are determined.

Key words: graph entropy, hypergraph, Laplacian degree

中图分类号:

O157.5

卢鹏丽, 薛玉龙. 基于拉普拉斯度的k-均匀超图的图熵极值[J]. 兰州理工大学学报, 2021, 47(3): 150-155.

LU Peng-li, XUE Yu-long. Extremality of graph entropy based on Laplacian degrees of k-uniform hypergraphs[J]. Journal of Lanzhou University of Technology, 2021, 47(3): 150-155.

参考文献

[1] FAN Y Z,TAN Y Y,PENG X X,et al.Maximizing spectralradii of uniform hypergraphs with few edges [J].Discussiones Mathematicae Graph Theory,2016,36(4):845-856.
[2] LI H,SHAO J Y,QI L.The extremal spectral radii of k-uniform supertrees [J].Journal of Combinatorial Optimization,2016,32(3):741-764.
[3] HU S,QI L,SHAO J Y.Cored hypergraphs,power hypergraphs and their Laplacian H-eigenvalues [J].Linear Algebra and Its Applications,2013,439(10):2980-2998.
[4] CAO S,DEHMER M,SHI Y.Extremality of degree-based graph entropies [J].Information Sciences,2014,278:22-33.
[5] SHANNON C E,WEAVER W,WIENER N.The mathematical theory of communication [M].Urbana,USA:University of Illinois Press,1949.
[6] DEHMER M.Information processing in complex networks:Graph entropy and information functionals [J].Applied Mathematics and Computation,2008,201(1/2):82-94.
[7] DAS K,DEHMER M.A conjecture regarding the extremal values of graph entropy based on degree powers [J].Entropy,2016,18(5):183-191.
[8] HU D,LI X L,LIU X G,et al.Extremality of graph entropy based on degrees of uniform hypergraphs with few edges [J].Acta Mathematica Sinica-English Series,2019,35(7):1238-1250.
[9] DAS K,SHI Y.Some properties on entropies of graphs [J].Match Communications Mathematical Computer Chemistry,2017,78(2):259-272.
[10] CHEN Z Q,DEHMER M,EMMERTS-STREIB F,et al.Entropy of weighted graphs with randic weights [J].Entropy,2015,17(6):3710-3723.
[11] LI X,WEI M.Graph entropy:Recent results and perspectives [J].Mathematical Foundations and Applications of Graph Entropy,2016,6:133-182.
[12] WAN P,TU J,DEHMER M,et al.Graph entropy based on the number of spanning forests of c-cyclic graphs [J].Applied Mathematics and Computation,2019,363:124616.
[13] RODRIGUEZ J A.On the Laplacian spectrum and walk-regular hypergraphs [J].Linear and Multilinear Algebra,2003,51(3):285-297.
[14] MARSHALL A W,OLKIN I,AMOLD B C.Inequalities:theory of majorization and its applications [M].New York:Academic press,1979.