一类k-正则图的生成树数目与熵  

Number of spanning trees of a class of k-regular graph and its entropy

作　　者：贾环身 吴廷增[1] JIA Huan-shen;WU Ting-zeng(School of Mathematics and Statistics,Qinghai Nationality University,Xining 810007,China)

机构地区：[1]青海民族大学数学与统计学院,西宁810007

出　　处：《哈尔滨商业大学学报（自然科学版）》2020年第4期475-478,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然基金项目(No.11761056).

摘　　要：若图G的一个生成子图T是一棵树,则称T为G的一棵生成树;若T为森林,则称它为G的一个生成森林.生成树是表征网络结构性质的一个重要物理量,网络中生成树越多,则网络越健壮.提出了一个k-正则图构成的小世界网络模型,介绍了其概念及演化过程,计算了k-正则图的相关拓扑特性,例如直径、聚类系数等,给出了此类k-正则图的生成树数目计算方法,得出生成树数目公式及熵.A spanning subgraph of a graphGis a treeT,it is called a spanning tree. IfTis a forest,it is called a spanning tree of the graphG. Spanning tree is an important quantity characterizing the structural properties of a network. The more spanning trees in a network,the more robust the network is. In this paper,a small world network model composed of k-regular graph was proposed. The concept and evolution process were introduced. This paper introduced the concept and evolving process and determine the relevant topological characteristics of thek-regular graph,such as diameter and clustering coefficient. Gave a calculation method of number of spanning trees in such four regular network and derived the formulas and the entropy of number of spanning trees.

关 键 词：K-正则图 小世界网络 图论 生成树 生成森林 熵 

分 类 号：O29[理学—应用数学]