正则m叉树T的S^((n))={K_i:1≤i≤n}-因子数的递归公式

A Recurrence Formula for the S^((n))-Factoring Number of a Regular m -furcating tree

在正则m叉树T中,删除K2及端点关联边,通过所得子正则m叉树中分枝点、叶数和m之间内在联系,本文导出正则m叉树T的S^(m)={Ki:1≤i≤n}-因子数递归公式.特别当m=2时,正则2叉树递归公式为:At=A_(t/2)~2+2A_(t/4)~2 A_(t/2),t为正则2叉树T的叶数.

For a regular m-furcating tree, the authors derive a recurrence formula of the number of its S(n)= {Ki: 1<i<n}-factor through analysing the relation among i,t and m of sub-furcating trees. Specially, m = 2, the recurrence formula of a regular binary tree is as follows; A,=A_t/4~2+ 2A_t/4~2 At/2, with initial conditions: A2= 3, A4 = 15.