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

## Institution

Morehead State University

## 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.

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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.