On the number of spanning trees of Kn and Km, n

The object of this paper is to introduce a new technique for showing that the number of labelled spanning trees of the complete bipartite graph K m, n is | T( m, n)| = m n − 1 n m − 1 . As an application, we use this technique to give a new proof of Cayley's formula | T( n)| = n n − 2 , for the...

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Bibliographic Details
Published inDiscrete mathematics Vol. 84; no. 2; pp. 205 - 207
Main Author Abu-Sbeih, Moh'd Z.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.09.1990
Elsevier
Subjects
Combinatorics. Ordered structures
Exact sciences and technology
Mathematics
Sciences and techniques of general use
Vertex(graph)
Bipartite graph
Spanning tree
Enumeration(counting)
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Summary:The object of this paper is to introduce a new technique for showing that the number of labelled spanning trees of the complete bipartite graph K m, n is | T( m, n)| = m n − 1 n m − 1 . As an application, we use this technique to give a new proof of Cayley's formula | T( n)| = n n − 2 , for the number of labelled spanning trees of the complete graph K n .
ISSN:0012-365X
1872-681X
DOI:10.1016/0012-365X(90)90377-T