Triangle-Y Families of Complete Graphs

Abstract

I attempt to determine the triangle-y (TY) family of any given complete graph. I present a method for determining the number of TY cousins on any level of the family diagram, and give sizes for the first five levels of any complete graph, with an upper bound for the sixth. I explain how the number of levels can be determined for complete graphs, and describe a possible method for determining the number of cousins at any level in general on a complete graph of arbitrary size.