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Wright's formulae for the number of connected sparsely edged graphs

โœ Scribed by P. M. D. Gray; A. M. Murray; N. A. Young


Publisher
John Wiley and Sons
Year
1977
Tongue
English
Weight
161 KB
Volume
1
Category
Article
ISSN
0364-9024

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โœฆ Synopsis


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.


๐Ÿ“œ SIMILAR VOLUMES


The number of connected sparsely edged g
โœ E. M. Wright ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 472 KB

## Abstract An (__n, q__) graph has __n__ labeled points, __q__ edges, and no loops or multiple edges. The number of connected (__n, q__) graphs is __f(n, q)__. Cayley proved that __f(n, n__^โ€1^) = __n__^nโˆ’2^ and Renyi found a formula for __f(n, n)__. Here I develop two methods to calculate the exp

The number of connected sparsely edged g
โœ E. M. Wright ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 306 KB

The number of nonseparable graphs on n labeled points and q lines is u(n, 9). In the second paper of this series an exact formula for u(n, n + k) was found for general n and successive (small) k. The method would give an asymptotic approximation for fixed k as n + 30. Here an asymptotic approximatio

The number of connected sparsely edged g
โœ E. M. Wright ๐Ÿ“‚ Article ๐Ÿ“… 1980 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 413 KB

## Abstract The number of connected graphs on __n__ labeled points and __q__ lines (no loops, no multiple lines) is __f(n,q).__ In the first paper of this series I showed how to find an (increasingly complicated) exact formula for __f(n,n+k)__ for general __n__ and successive __k.__ The method woul

The number of connected sparsely edged g
โœ E. M. Wright ๐Ÿ“‚ Article ๐Ÿ“… 1978 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 215 KB

A smooth graph is a connected graph without endpoints; f (n, q ) is the number of connected graphs, v(n, q ) is the number of smooth graphs, and u(n, q) is the number of blocks on n labeled points and q edges: wk, V,, and u k are the exponential generating functions of f(n, n + k ) , v(n, n + k). an

The Number of Removable Edges in 3-Conne
โœ Su Jianji ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 147 KB

An edge of a 3-connected graph G is said to be removable if G&e is a subdivision of a 3-connected graph. Holton et al. (1990) proved that every 3-connected graph of order at least five has at least W(|G| +10)ร‚6X removable edges. In this paper, we prove that every 3-connected graph of order at least

An Asymptotic Formula for the Number of
โœ Roger F. Wheeler ๐Ÿ“‚ Article ๐Ÿ“… 1962 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 205 KB

The present article is really a continuation of the author's earlier paper [,l] on this subject. The line of investigation described previously is rounded off by deriving some further numcrical results, which include, in particular, an asymptotic fonnula for the number of complete propositional conn