Title

Classifying and Documenting TY-Realizable Trees

Authors

Scott McCalla

Document Type

Article

Publication Date

2011

Abstract

This project centers around Triangle Y - moves (TY-moves). TY-moves are an operation on graphs (collections of vertices and edges), where we remove the edges AB, AC, and BC of a triangle with vertices A, B, and C, insert a new vertex D, then insert the edges AD, BD, and CD. We can move between several different graphs by doing TY-moves and Y Triangle - moves (YT-moves), and we can organize these graphs by placing graphs with different numbers of vertices above or below each other (as a TY-move adds a vertex). We call this a family diagram. We call a graph G TY-realizable if we can find a family of graphs that has G for a family diagram. We have been going through graphs looking for a way to characterize all trees, whether it is the case that they all are the family diagram of some graph, or that only some types of graphs are TY-realizable. We have categorized all trees with four and fewer vertices as TY realizable as well as some with five or more.

Advisor

Ramin Naimi

Department

math

Support

National Science Foundation Grant to Prof. Naimi

This document is currently not available here.

Share

COinS