dc.contributor.author | Cox, Danielle | |
dc.date.accessioned | 2013-06-24T12:55:37Z | |
dc.date.available | 2013-06-24T12:55:37Z | |
dc.date.issued | 2013-06-24 | |
dc.identifier.uri | http://hdl.handle.net/10222/27775 | |
dc.description.abstract | The all terminal reliability of a graph G is the probability that at least a spanning tree
is operational, given that vertices are always operational and edges independently
operate with probability p in [0,1]. In this thesis, an investigation of all terminal
reliability is undertaken. An open problem regarding the non-existence of optimal
graphs is settled and analytic properties, such as roots, thresholds, inflection points,
fixed points and the average value of the all terminal reliability polynomial on [0,1]
are studied.
A new reliability problem, the k -clique reliability for a graph G is introduced. The
k-clique reliability is the probability that at least a clique of size k is operational, given
that vertices operate independently with probability p in [0,1] . For k-clique reliability
the existence of optimal networks, analytic properties, associated complexes and the
roots are studied. Applications to problems regarding independence polynomials are
developed as well. | en_US |
dc.language.iso | en | en_US |
dc.subject | Polynomials | en_US |
dc.subject | Combinatorics | en_US |
dc.subject | Network reliability | en_US |
dc.title | On Network Reliability | en_US |
dc.date.defence | 2013-06-03 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Doctor of Philosophy | en_US |
dc.contributor.external-examiner | Dr. Gary Gordon | en_US |
dc.contributor.graduate-coordinator | Dr. Sara Faridi | en_US |
dc.contributor.thesis-reader | Dr. Karl Dilcher | en_US |
dc.contributor.thesis-reader | Dr. Richard Nowakowski | en_US |
dc.contributor.thesis-supervisor | Dr. Jason Brown | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |