On the numbers of spanning trees and Eulerian tours in generalized de Bruijn graphs
β Scribed by Xueliang Li; Fuji Zhang
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 756 KB
- Volume
- 94
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
A rccenl theorem due to W'aller is applied to the mokculnr gmph of a typical conjugtcd system (naphthalene) in order to demonstrate the enumeration of spanning trees, on each of which a "ring current" calculation may be based.
The following asymptotic estimation of the maximum number of spanning trees f k (n) in 2kregular circulant graphs ( k ΓΊ 1) on n vertices is the main result of this paper: )) , where
For a connected graph G, let ~-(G) be the set of all spanning trees of G and let nd(G) be the number of vertices of maximum degree in G. In this paper we show that if G is a cactus or a connected graph with p vertices and p+ 1 edges, then the set {na(T) : T C ~-(G)) has at most one gap, that is, it
A new calculation is given for the number of spanning trees in a family of labellec; graphs considered by Kleitman and Golden, and for a more general class of such graphs.
An algebraic approach to enumerate the number of cycles of short length in the de Bruijn-Good graph Gn is given and the following theorem is proved. where ~)k,m--1 is defined to be the number of positive integers l <<-k satisfying (k, l) <<-m -1, l~(q) is the M6bius function, dt = (k, l), e~ = 0 or