关于K圈标号图的计数

本文研究含K个圈的标号图的计数问题,得出了有n个标定顶点且有K个交于一点的圈的连通图的计数公式,并得到了双圈连通标号图的计数公式,从而解决了K-2时连通图的计数问题。

Enumeration on the Labeled Graphs With K Cycles

In this paper, we continue the study of the enumeration problems of labeled graphs with k cycles that Tomscu didn't solve. A counting formula for the connected graphs with n labeled vertices and k cycles intersecting at a point is given. As an application, together with Tomscu's result we solve the enumeration problem of labeled connected graphs with two cycles.