厦门大学学报（自然科学版）2016，Vol.55Issue(4)：554-557,4.DOI:10.6043/j.issn.0438-0479.201512026
有关对称无权图生成树数目的拆分定理
The Factorization Theorems on the Number of Spanning Trees of Graphs with Some Symmetry
摘要
Abstract
Let G be a plane graph with reflective symmetry.Ciucu,et al,proved a factorization theorem on the number of spanning trees of G.That is,the number of spanning treesof G can be expressed in terms of the product of the number of spanning trees of two smaller graphs.In this paper,we introduce a graph transformation and discuss its effect on the number of spanning trees,then by the matrix-tree theorem we give a short proof of above-mentioned factorization theorem.Motivated by a factorization theorem on the sum of weights of spanning trees of weighted graphs with some symmetry in Zhang et al,we further provide an equivalent factorization formula on the number of spanning trees of unweighted graphs with some symmetry.关键词
生成树数目/矩阵-树定理/对称性/平面图Key words
spanning trees number/matrix-tree theorem/symmetry/plane graph分类
数理科学引用本文复制引用
龚和林,王伟..有关对称无权图生成树数目的拆分定理[J].厦门大学学报（自然科学版）,2016,55(4):554-557,4.基金项目
国家自然科学基金(11271307,11561058) （11271307,11561058）
广西高校数学与统计模型重点实验室开放课题 （）
