## Morehead State University

# STUDY 2: The Equivalence Number and Transit Graphs for Chessboard Graphs

## Institution

Morehead State University

## Faculty Advisor/ Mentor

Robin Blankenship; R. Doug Chatham; R. Duane Skaggs

## Abstract

The queens graph can be considered as a system of routes called a "transit graph", where two vertices are connected by an edge if and only if there is a path from one vertex to the other in at least one of the routes. The "equivalence number" is the smallest number of routes needed to form a given transit graph. The study of transit graphs provides a new perspective to the analysis of chessboard graphs with obstacles, and the approach extends to other chess pieces and other types of boards.

STUDY 2: The Equivalence Number and Transit Graphs for Chessboard Graphs

The queens graph can be considered as a system of routes called a "transit graph", where two vertices are connected by an edge if and only if there is a path from one vertex to the other in at least one of the routes. The "equivalence number" is the smallest number of routes needed to form a given transit graph. The study of transit graphs provides a new perspective to the analysis of chessboard graphs with obstacles, and the approach extends to other chess pieces and other types of boards.