Secker, Peter Ronald (1989). Feasibility algorithms for distance-biregular graphs. University of Birmingham. Ph.D.
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Secker1990PhD.pdf
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Abstract
A distance-biregular graph is a finite, undirected bipartite graph where any two vertices in the same part of the bipartition have the same intersection array. In this thesis we find necessary conditions for a pair of arrays to correspond to a distance-biregular graph and use these to construct an algorithm for generating all pairs of feasible arrays corresponding to possible graphs of girth four and smallest valency
\(b_0\)\(' < 20\). The feasible arrays with \(b_0\)\(' < 10\) are analysed in Chapters 5 and 6; those with \(10 \leq b_0\)\(' < 20\) are listed in Appendix II. Our results raised a number of interesting questions which are listed at the end of Appendix II.
| Type of Work: | Thesis (Doctorates > Ph.D.) | ||||||
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| Award Type: | Doctorates > Ph.D. | ||||||
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| Licence: | All rights reserved | ||||||
| College/Faculty: | Faculties (to 1997) > Faculty of Science | ||||||
| School or Department: | Department of Mathematics | ||||||
| Funders: | Other | ||||||
| Other Funders: | Science and Engineering Research Council | ||||||
| Subjects: | Q Science > QA Mathematics | ||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/14170 |
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