The number of connected sparsely edged graphs
The number of connected sparsely edged graphs
复制标题
稀疏边连通图的数量
作者：
E. Wright
（n，q）图具有n个标记点，Q边缘，没有循环或多个边缘。 ）= Nn -2和Renyi找到了F（n，n）的公式。 n，n + k）对于n，第一个方法是相对于k的经常性方法，并且适用于机器计算，但本身并不提供可以无限期继续的（还原）方法。效率降低得多，对于K大于2或3的K确实是不切实际的，但是它提供了缺少的证据，证明生成功能是特定形式的，因此可以继续所有K，仅遵守所有K。机器。
An (n, q) graph has n labeled points, q edges, and no loops or multiple edges. The number of connected (n, q) graphs is f(n, q). Cayley proved that f(n, n-1) = nn−2 and Renyi found a formula for f(n, n). Here I develop two methods to calculate the exponential generating function of f(n, n + k) for particular k and so to find a formula for f(n, n + k) for general n. The first method is a recurrent one with respect to k and is well adapted for machine computation, but does not itself provide a proof that it can be continued indefinitely. The second (reduction) method is much less efficient and is indeed impracticable for k greater than 2 or 3, but it supplies the missing proof that the generating function is of a particular form and so that the first method can be continued for all k, subject only to the capacity of the machine.