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Connectivity of random graphs

Published online by Cambridge University Press:  14 July 2016

Chang C. Y. Dorea
Chang C. Y. Dorea*
Affiliation:
Universidade de Brasilia
*
∗ Permanent address: Depto de Matemática-IE, Universidade de Brasilia, 70910 Brasilia DF, Brazil. From 1982 to 1984 the author will be a Visiting Scholar at Iowa State University.
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Abstract

We consider a random field {Xij, i, j = 1, ···, n} where the random variables Xij takes on values 1 or 0. The collection {Xij} can be viewed as a random graph with nodes {1, ···, n} by interpreting Xij = 1 as the existence of an arc emanating from the node i to the node j. Such a representation will enable us to study ordered and unordered graphs, being also the general representation of a random graph. In this note the probability that the graph is connected is computed under the condition that ΣiXki=l for k = 1, · ··, n. This result extends Ross's recent theorems on connectivity of random graphs.

Keywords

RANDOM FIELDSPROBABILITY OF CONNECTIVITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 880 - 884
Copyright
Copyright © Applied Probability Trust 1982 

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References

[1] Busacker, R. G. and Saaty, T. L. (1965) Finite Graphs and Networks: an Introduction with Applications. McGraw-Hill, New York.Google Scholar
[2] Harris, B. (1960) Probability distributions related to random mappings. Ann. Math. Statist. 31, 1045–1062.Google Scholar
[3] Ross, S. M. (1981) A random graph. J. Appl. Prob. 18, 309–315.Google Scholar