## Stander Symposium Projects

#### Presenter(s)

Christian Steven Hemsath

This poster reflects research conducted as part of a course project designed to give students experience in the research process.

#### Description

A graph is a mathematical object that consists of two sets: a set of vertices and a set of edges. An edge joins two vertices and depicts a relationship between those vertices. The following is a project for MTH 466 - Graph Theory and Combinatorics. Consider each vertex in a graph being associated with a light and with a button. Each push of the button will change the state of the light from on to off, or from off to on. Additionally, the state of each vertex joined by an edge to the vertex in question is changed. Given a graph with all vertex lights on, does there exist a set of light buttons which, when pressed, will turn off all vertex lights? An exploration of several examples of this question for different graphs is presented. It will also be proven that, for any connected graph, there exists a sequence of light buttons which when pressed will turn off all vertex lights.

4-24-2019

#### Project Designation

Course Project

Aparna W. Higgins