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-
β¦ LIBER β¦
On the asymptotic behavior of the maximum number of spanning trees in circulant graphs
β Scribed by Lonc, Zbigniew; Parol, Krzysztof; Wojciechowski, Jacek M.
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 126 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0028-3045
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β¦ Synopsis
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
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Let Tp be any tree of order p and A ( T p ) stand for the maximum degree of the vertices of Tp. We prove the following theorem. "If A(Tp) 5 pi, where p > 2i, then Tp is i-placeable in Kp" is true if and only if i = 1, 2, and 3. 0 1996 John Wiley & Sons, Inc. Suppose G is a graph and V ( G ) , E ( G