半正则二部图的Kn-补图的生成树的一种计数公式
A Counting Formula for Spanning Trees of Kn-complemented Graphs of Semiregular Bipartite Graph
严秀蓉 1姚菊田1
作者信息
- 1. 绍兴文理学院 数理信息学院,浙江 绍兴 312000
- 折叠
摘要
设G是完全图Kn 的一个子图,G的Kn-补图是从Kn 删去子图G的所有边得到的图.利用Kirchhoff矩阵-树定理、矩阵的Schur补以及电网络等价理论,给出了半正则二部图的Kn-补图的生成树计数的一般行列式表达式.
Abstract
Let G be a semiregular bipartite subgraph of the complete graph Kn,and the Kn-complemented graph of G be the graph obtained by deleting all edges of the subgraph G from Kn.This research obtains the general counting determinant formula of the spanning tree of Kn-complemented graphs of semiregular bipartite graph based on the Kirchhoff matrix-tree theorem,the Schur complement of matrices,and the theory of electrical network equiv-alence.
关键词
二部图/半正则/电网络等价/Kirchhoff矩阵-树定理/Schur补Key words
bipartite graph/semiregularity/electric network equivalence/Kirchhoff matrix-tree theorem/Schur complemen引用本文复制引用
出版年
2024
NETL
NSTL
万方数据