# The Edge-Distinguishing Game

## TL;DR

This paper introduces the Edge-Distinguishing Game, a graph coloring game, analyzing winning strategies for specific graphs using game theory and computational methods.

## Contribution

It defines the edge-distinguishing chromatic number and determines winning strategies for particular graphs and families, combining game theory and computational approaches.

## Key findings

- Identified winning strategies for certain graphs.
- Defined the edge-distinguishing chromatic number.
- Applied computational methods to analyze the game.

## Abstract

In this paper, we introduce a graph coloring game called the Edge-Distinguishing Game (EDGe). The edge-distinguishing chromatic number of a graph is used to determine the moves each player can make. We determine which player has a winning strategy for particular graphs and graph families. Additionally, utilizing principles from game theory as well as previous work on a computational solution for the Game of Cycles.