Products and Factorizations of Graphs
| dc.contributor.advisor | Sabidussi, G. | |
| dc.contributor.author | Miller, Donald J. | |
| dc.contributor.department | Mathematics | en_US |
| dc.date.accessioned | 2016-06-28T16:33:27Z | |
| dc.date.available | 2016-06-28T16:33:27Z | |
| dc.date.issued | 1967-05 | |
| dc.description.abstract | It is shown that the cardinal product of graphs does not satisfy unique prime factorization even for a very restrictive class of graphs. It is also proved that every connected graph has a decomposition as a weak cartesian product into indecomposable factors and that this decomposition is unique to within isomorphisms. This latter result is established by considering a certain class of equivalence relations on the edge set of a graph and proving that this collection is a principal filter in the lattice of all equivalences. The least element of this filter is then used to decompose the graph into a weak cartesian product of prime graphs that is unique to within isomorphisms. | en_US |
| dc.description.degree | Doctor of Philosophy (PhD) | en_US |
| dc.description.degreetype | Thesis | en_US |
| dc.identifier.uri | http://hdl.handle.net/11375/19666 | |
| dc.language.iso | en_US | en_US |
| dc.subject | products, factorizations, graphs, prime, isomorphisms | en_US |
| dc.title | Products and Factorizations of Graphs | en_US |
| dc.type | Thesis | en_US |