Let G be a probabilistic (n,m) graph in which each vertex exists independently with fixed probability p , 0 < p < 1. Pair-connected reliability of G, denoted PC,(G;p), is the expected number of connected pairs of vertices in G. An (n.m) graph G is uniformly optimally reliable if PC,(G;p) 2 PC,(H;p) for all p, 0 < p < 1, over all (n,m) graphs H. It is shown that there does not exist a uniformly optimally reliable ( n m ) graph whenever n I m < -2n2/9. However, such graphs do exist for some other values of m. In particular, it is established that every complete k-partite pseudoregular graph on n vertices, 2 I k < n, is uniformly optimally reliable. 0 7993 by John Wiley & Sons, Inc.
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