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COUNTEREXAMPLES TO CONJECTURES FOR UNIFORMLY OPTIMALLY RELIABLE GRAPHS
Published online by Cambridge University Press: 01 April 2000
Abstract
In [7], several conjectures are listed about uniformly most reliable graphs, and, to date, no counterexamples have been found. These include the conjectures that an optimal reliable graph has degrees that are almost regular, has maximum girth, and has minimum diameter. In this article, we consider simple graphs and present one counterexample and another possible counterexample of these conjectures: maximum girth (i.e., maximize the length of the shortest circuit of the graph G) and minimum diameter (i.e., minimize the maximum possible distance between any pair of vertices).
- Type
- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 14 , Issue 2 , April 2000 , pp. 173 - 177
- Copyright
- © 2000 Cambridge University Press