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SOME CONJECTURED UNIFORMLY OPTIMAL RELIABLE NETWORKS

Published online by Cambridge University Press:  01 July 2000

Yontha Ath  and
Milton Sobel
Yontha Ath
Affiliation:
Department of Mathematics, Claremont Graduate University, Claremont, California 91711-6160
Milton Sobel
Affiliation:
Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, California 93106
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Abstract

We consider all-terminal reliability, one of the more popular models in the field of network reliability. A graph with n nodes and e edges, where the nodes are perfectly reliable and the edges survive independently with equal probability p, is said to be a uniformly optimally reliable graph if it has for all values of p (0 ≤ p ≤ 1) an equal or higher reliability among all graphs with the same number of nodes and edges. Boesch et al. [4] verified the existence of uniformly optimally reliable graphs for e = n − 1, e = n, e = n + 1, and e = n + 2; he has also given a conjecture for e = n + 3. Wang [8] proved this conjecture. In this article, we present four new infinite families of graphs that we conjecture to be uniformly optimal.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 3 , July 2000 , pp. 375 - 383
Copyright
© 2000 Cambridge University Press

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