Physical Sciences and Mathematics Commons^™

Cancellation Properties Of Direct Products Of Digraphs, Katherine Toman

Theses and Dissertations

This paper discusses the direct product cancellation of digraphs. We define the exact conditions on G such that GxK=HxK implies G=H. We focus first on simple equations such as GxK_2=HxK_2 where K_2 denotes a single arc and then extend this to the more general situation, GxK = HxK. Our results are achieved by using a “factorial” operation on graphs, which is in some sense analogous to the factorial of an integer.