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.
โฆ LIBER โฆ
The number of spanning trees of a graph
โ Scribed by Kinkar C Das,Ahmet S Cevik,Ismail N Cangul
- Book ID
- 121618794
- Publisher
- Hindawi Publishing Corporation
- Year
- 2013
- Tongue
- English
- Weight
- 207 KB
- Volume
- 2013
- Category
- Article
- ISSN
- 1025-5834
No coin nor oath required. For personal study only.
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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