Physical Sciences and Mathematics Commons^™

Uniqueness Of Bipartite Factors In Prime Factorizations Over The Direct Product Of Graphs, Owen Puffenberger

Theses and Dissertations

While it has been known for some time that connected non-bipartite graphs have unique prime factorizations over the direct product, the same cannot be said of bipartite graphs. This is somewhat vexing, as bipartite graphs do have unique prime factorizations over other graph products (the Cartesian product, for example). However, it is fairly easy to show that a connected bipartite graph has only one prime bipartite factor, which begs the question: is such a prime bipartite factor unique? In other words, although a connected bipartite graph may have multiple prime factorizations over the direct product, do such factorizations contain the …