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The second moment of the complexity of a graph

Published online by Cambridge University Press:  26 February 2010

J. W. Moon
J. W. Moon
Affiliation:
University College, and London.
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Extract

A graph consists of a set of vertices some pairs of which are joined by a single edge. A tree is a graph with the property that each pair of vertices is connected by precisely one path, i.e., a sequence of distinct vertices joined consecutively by edges. The complexity c of a graph G(n, k) with n vertices and k edges is the number of trees with n vertices which are subgraphs of G(n, k). The distribution of c over the class of all graphs G(n, k) is of physical interest because it throws light on the classical many-body problem. (See, e.g. [9].) Ford and Uhlenbeck [3] gave numerical data which suggested that the distribution of c tends to normality for increasing n if k is near No moments higher than the first were known in general and they remarked in [4] that even “the second would be worth knowing”. The main object in this paper is to derive a formula for the second moment of c.

Type
Research Article
Information
Mathematika , Volume 11 , Issue 2 , December 1964 , pp. 95 - 98
Copyright
Copyright © University College London 1964

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References

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