王氏代数的推论和m阶全图的树的数量表达式

The Lemmas on Wong Algebra and a Formula on Tree Quantity of a m-Order Complete Graph

在文献［１］提出的求一个图的全部树的方法中，王氏代数被用以筛除相关元素（相关树支）。此文将进一步讨论王氏代数的有关定义和运算规则，给出了部分相关和子相关符号向量等概念。文中提出的４个推论使王氏代数得以在求图的树的算法中得到系统的应用。在分析了ｍ阶全图的关联矩阵的特性后，定理１给出了其具有的树数量的表达式。

In paper a method of listing all tree of a graph was presented and in this method Wong Algebra was employed to delete Relative Tree Branches In our paper we give out some new Wong Algebra's definitions and rules, such as partial relative symbol vector , complete relative symbol vector, symbol vector addition and multiplication operation etc The four lemmas obtained can be used to simplify the method of listing all trees of a graph After analysing the property of complete graph, a formula of tree quantity of a m-order complete graph is given in Theorem 1