A Sharp Upper Bound for the Number of Spanning Trees of a Graph
β Scribed by Kinkar Ch. Das
- Publisher
- Springer Japan
- Year
- 2007
- Tongue
- English
- Weight
- 85 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
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.
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.
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Let G be a connected and simple graph, and let i(G) denote the number of stable sets in G. In this letter, we have presented a sharp upper bound for the i(G)-value among the set of graphs with k cut edges for all possible values of k, and characterized the corresponding extremal graphs as well.