#### Title

Lights Out - An Exploration of Domination in Graph Theory

#### Files

#### 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.

#### Publication Date

4-24-2019

#### Project Designation

Course Project

#### Primary Advisor

Aparna W Higgins

#### Primary Advisor's Department

Mathematics

#### Keywords

Stander Symposium poster

#### Recommended Citation

"Lights Out - An Exploration of Domination in Graph Theory" (2019). *Stander Symposium Posters*. 1558.

https://ecommons.udayton.edu/stander_posters/1558

## Comments

Presenter: Christian Steven Hemsath