Graphs on unlabelled nodes with a given number of edges
Graphs on unlabelled nodes with a given number of edges
复制标题
具有给定边数的未标记节点上的图
DOI：
10.1007/bf02392023
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发表时间：
1971
期刊：
影响因子：
3.7
通讯作者：
E. Wright
中科院分区：
文献类型：
--
作者：
E. Wright
我们写Tnq为n个未标记节点上的不同图的数量，只有q条边。对于大的n，我们将找到T，q的一个渐近近似，并确定它适用的q的精确范围。在我们考虑的图中，每对节点都只有一条无向边连接或没有连接，尽管我们的方法显然可以扩展到其他类型的图。如果节点被标记，则有N条可能的边，其中N= n（n-1）/2，并且只有q条边的图的数量为
We write Tnq for the number of different graphs on n unlabelled nodes with just q edges. We shall find an asymptotic approximation to T, q for large n and determine the exact range for q for which it holds good. In the graphs we consider, every pair of nodes is joined by just one undirected edge or not so joined, though our method can clearly be extended to other types of graph. If the nodes are labelled, there are N possible edges, where N= n (n-1)/2, and the number of graphs with just q edges is