基于电等效转换的一类分形网络生成树枚举  

Enumeration of Spanning Trees of a Family of Fractal Networks Based on Electrically Equivalent Transformation

作　　者：许文豪[1] 孙伟刚[1] XU Wenhao;SUN Weigang(School of Science,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2018年第1期99-102,共4页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(61673144)

摘　　要：提出一大类分形网络模型并计算其生成树数目。首先利用电等效转换,得到了边权重的变化规律和生成树数目在原始网络和电等效转换后网络之间的迭代关系,同时给出了生成树枚举的解析表达式,其次用矩阵树定理验证了所得解析结果的正确性,最后拓展了分形网络的模型。This paper proposes a family of fractal networks and calculates its number of spanning trees.The rules of weighted edges and relationship of enumerating spanning trees between the original and corresponding equivalent networks are obtained.The exact solution of spanning trees is also derived.The obtained results are verified by the matrix-tree theorem.

关 键 词：拉普拉斯矩阵 生成树 电等效转换 

分 类 号：O157.5[理学—数学]