Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/19666
Title: | Products and Factorizations of Graphs |
Authors: | Miller, Donald J. |
Advisor: | Sabidussi, G. |
Department: | Mathematics |
Keywords: | products, factorizations, graphs, prime, isomorphisms |
Publication Date: | May-1967 |
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. |
URI: | http://hdl.handle.net/11375/19666 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Miller_Donald_J._1967May_Ph.D..pdf | 2.3 MB | Adobe PDF | View/Open |
Items in MacSphere are protected by copyright, with all rights reserved, unless otherwise indicated.