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Expected Value Expansions in Random Subgraphs with Applications to Network Reliability

Published online by Cambridge University Press:  01 December 1998

KYLE SIEGRIST
Affiliation:
University of Alabama in Huntsville, Huntsville, AL 35899, USA (e-mail: siegrist@math.uah.edu)

Abstract

Subgraph expansions are commonly used in the analysis of reliability measures of a failure-prone graph. We show that these expansions are special cases of a general result on the expected value of a random variable defined on a partially ordered set; when applied to random subgraphs, the general result defines a natural association between graph functions. As applications, we consider several graph invariants that measure the connectivity of a graph: the number of connected vertex sets of size k, the number of components of size k, and the total number of components. The expected values of these invariants on a random subgraph are global performance measures that generalize the ones commonly studied. Explicit results are obtained for trees, cycles, and complete graphs. Graphs which optimize these performance measures over a given class of graphs are studied

Type
Research Article
Copyright
1998 Cambridge University Press

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