#### Presenter(s)

Noah Jacob Kilps

#### Files

Download Project (282 KB)

#### Description

This project is for MTH 466, Graph Theory and Combinatorics. A graph is a mathematical object that consists of two sets, a set of vertices and a set of edges in which an edge between two vertices denotes a relationship between those vertices. A dominating set of a graph G is a set of vertices S such that every vertex of G is a neighbor of some vertex in S. The domination number is the minimum number of vertices in a dominating set S. Let F be a graph whose vertex set is partitioned into two sets: blue vertices and red vertices. Let v be a designated blue vertex of F. An F-coloring of a graph G is a red-blue coloring of the vertices of G in which every blue vertex u belongs to a copy of F rooted at v. The F-domination number is the minimum number of red vertices in an F-coloring of G. We will compare the properties of the domination number and the F-domination number.

#### Publication Date

4-22-2021

#### Project Designation

Course Project

#### Primary Advisor

Aparna W. Higgins

#### Primary Advisor's Department

Mathematics

#### Keywords

Stander Symposium project, College of Arts and Sciences

#### Recommended Citation

"Domination and F-Domination" (2021). *Stander Symposium Projects*. 2210.

https://ecommons.udayton.edu/stander_posters/2210

## Comments

This poster reflects research conducted as part of a course project designed to give students experience in the research process. Course: MTH 466