Steinhaus Graphs and Pendent Vertices (thesis)

Abstract

Steinhaus graphs have many interesting properties, yet there are many things about them that are not yet known. In [1], a formula was discovered for the total number of Steinhaus graphs on 11 vertices with at least one pendent vertex. Our research goal was to try to further characterize this result. Can we describe the number of Steinhaus graphs on n vertices with exactly k pendent vertices? Let P(n,k) be the number of Steinhaus graphs on n vertices with k pendent vertices. Our task was to find an explicit formula for it. [introduction]