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. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/19666 |
| Date | 05 1900 |
| Creators | Miller, Donald J. |
| Contributors | Sabidussi, G., Mathematics |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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