Formulas for the number of trees in certain incomplete graphs
โ Scribed by S.D. Bedrosian
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 192 KB
- Volume
- 289
- Category
- Article
- ISSN
- 0016-0032
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โฆ Synopsis
A concise summary is given of the standardized incomplete graphs denoted as the r, p, m and s series. Bercovici's recent general formula for the number of trees in the m series is considered and the corresporLdin,g gen,eral formula for the s series is given.
๐ SIMILAR VOLUMES
## Abstract We have written computer programs to determine exactly the coefficients in Wright's formula for __f(n, n + k)__, the number of connected sparsely edged labeled graphs (see preceding paper), and used them up to __k__ = 24. We give the results up to __k__ = 7.
In this paper it is shown that for every fixed k 1> 3, G(n; d = k) = 2(~) (6.2 -k + o(1))", where G(n; d = k) denotes the number of graphs of order n and diameter equal to k. It is also proved that for every fixed k>~2, lim,~G(n;d=k)/G(n;d=k+ 1)=lim.o~G(n;d=n-k)/ G(n;d=n-k+ 1)= oo hold.
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.