Enumeration of Labelled (k,m)-Trees

The enumeration of labelled spanning trees of Km, n

Using a bijection to decompose a labelled rooted bipartite tree into several ones with smaller size and their exponential generating functions, this paper concerns the number of labelled spanning trees of the complete bipartite graph K m,n .

Enumeration of Some Labelled Trees

In this paper we are interesting in the enumeration of rooted labelled trees according to the relationship between the root and its sons. Let Tn;k be the family of Cayley trees on n] such that the root has exactly k smaller sons. In a rst time we give a bijective proof of the fact that jTn+1;kj = ? n k n n?k. Moreover, we use the family Tn+1;0 of Cayley trees for which the root is smaller than ...

The Application of Lagrangian Methods to the Enumeration of Labelled Trees with Respect to Edge Partition

Asymptotic Enumeration of Labelled Graphs by Genus

We obtain asymptotic formulas for the number of rooted 2-connected and 3connected surface maps on an orientable surface of genus g with respect to vertices and edges simultaneously. We also derive the bivariate version of the large facewidth result for random 3-connected maps. These results are then used to derive asymptotic formulas for the number of labelled k-connected graphs of orientable g...

Enumeration of Weighted Trees

In weighted trees, all edges are endowed with positive integral weight. We enumerate weighted bicolored plane trees according to their weight and number of edges. 1 Preliminaries This paper is not intended for publication: it does not contain difficult results, and the proofs use only standard and well-known techniques. However, the results stated below have their place in the context of the st...