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.
The number of DFAs for a given spanning tree
β Scribed by P. Babaali, E. Carta-Gerardino, C. Knaplund
- Book ID
- 120780501
- Publisher
- Springer US
- Year
- 2013
- Tongue
- English
- Weight
- 549 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0920-8542
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## Abstract Let __G__ be a graph and __f__ be a mapping from __V__(__G__) to the positive integers. A subgraph __T__ of __G__ is called an __f__βtree if __T__ forms a tree and __d__~__T__~(__x__)β€__f__(__x__) for any __x__β__V__(__T__). We propose a conjecture on the existence of a spanning __f__βt
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