On the equivalences of the wheel W5, the prism P and the bipyramid B5
Hossein Shahmohamad · RIT Scholar Works (Rochester Institute of Technology) · 2003
The main results of this paper are the discovery of infinite families of flow equivalent pairs of B5 and W5 amallamorphs and infinite families of chromatically equivalent pairs of P and W*5 homeomorphs, where B5 is K5 with one edge deleted, P is the Prism graph and W5 is the join of K1 and a cycle on 4 vertices. Six families of B5 amallamorphs, with two families having 6 parameters, and 9 families of W5 amallamorphs, with one family having 4 parameters, are discovered. Since B5 and W5 are both planar, all these results obtained can be stated in terms of chromatically equivalent pairs of B*5 and W*5 homeomorphs. Also three conjectures are made about non-existence of flow-equivalent amallamorphs or chromatically equivalent homeomorphs of certain graphs (Refer to PDF file for exact formulas).