#### Title

Edge-distinguishing colorings of graphs in Maker-Breaker games

#### Presentation Type

Presentation

#### Faculty Mentor’s Full Name

Jenny McNulty

#### Faculty Mentor’s Department

Mathematical Sciences

#### Abstract

A Maker-Breaker game is one where the Maker tries to accomplish a defined goal while the Breaker tries to prevent this. The particular Maker-Breaker game under investigation is played on a graph, which is a mathematical object composed of vertices and edges. One colors the graph by assigning a color to each of the edges. A coloring of the graph is edge-distinguishing if the edges are colored in such a way as to force asymmetry on the graph. The Maker's goal is to make the coloring edge-distinguishing. The players take turns coloring each uncolored edge with a color of their choice. The number of colors each player can choose from is at least the graph's distinguishing number, which is the minimum number of colors needed to make an edge-distinguishing coloring. The study of Maker-Breaker games and edge-distinguishing colorings of graphs are both young and active areas of research. To examine the two concepts together is novel. This approach uses previous work on edge-distinguishing colorings of graphs and extends the scope of study of Maker-Breaker games.

#### Category

Physical Sciences

Edge-distinguishing colorings of graphs in Maker-Breaker games

UC 326

A Maker-Breaker game is one where the Maker tries to accomplish a defined goal while the Breaker tries to prevent this. The particular Maker-Breaker game under investigation is played on a graph, which is a mathematical object composed of vertices and edges. One colors the graph by assigning a color to each of the edges. A coloring of the graph is edge-distinguishing if the edges are colored in such a way as to force asymmetry on the graph. The Maker's goal is to make the coloring edge-distinguishing. The players take turns coloring each uncolored edge with a color of their choice. The number of colors each player can choose from is at least the graph's distinguishing number, which is the minimum number of colors needed to make an edge-distinguishing coloring. The study of Maker-Breaker games and edge-distinguishing colorings of graphs are both young and active areas of research. To examine the two concepts together is novel. This approach uses previous work on edge-distinguishing colorings of graphs and extends the scope of study of Maker-Breaker games.