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The number of spanning trees of a graph

โœ Scribed by Jianxi Li; Wai Chee Shiu; An Chang

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
387 KB
Volume
23
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

In this paper, we present some sharp upper bounds for the number of spanning trees of a connected graph in terms of its structural parameters such as the number of vertices, the number of edges, maximum vertex degree, minimum vertex degree, connectivity and chromatic number.

๐Ÿ“œ SIMILAR VOLUMES

On the number of spanning trees in a mol
On the number of spanning trees in a molecular graph
โœ R.B. Mallion ๐Ÿ“‚ Article ๐Ÿ“… 1975 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 444 KB

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.

On numbers of vertices of maximum degree
On numbers of vertices of maximum degree in the spanning trees of a graph
โœ Jerzy Topp; Preben D. Vestergaard ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 611 KB

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

Calculating the number of spanning trees
Calculating the number of spanning trees in a labeled planar molecular graph whose inner dual is a tree
โœ P. E. John; R. B. Mallion ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 496 KB ๐Ÿ‘ 3 views

The quantum mechanical relevance of the concept of a spanning tree extant within a given molecular graph-specifically, one that may be considered to represent the carbon-atom connectivity of a particular (planar) conjugated system-was first explicitly pointed out by Professor Roy McWeeny in his now-

Finding the Graph with the Maximum Numbe
Finding the Graph with the Maximum Number of Spanning Trees
โœ George Moustakides; Samuel D. Bedrosian ๐Ÿ“‚ Article ๐Ÿ“… 1980 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 328 KB

The problem is to determine the linear graph that has the maximum number of spanning trees, where only the number of nodes N and the number of branches B are prescribed. We deal with connected graphs G(N, B) obtained by deleting D branches from a complete graph KN. Our solution is for D less than or