Cops and Robbers on Toroidal Chess Graphs

TL;DR

This paper studies various versions of the Cops and Robbers game played on toroidal chess graphs, determining the cop number for each variant based on different chess piece movements.

Contribution

It provides a complete determination of the cop number for multiple Cops and Robbers variants on toroidal chess graphs with different piece-move rules.

Findings

Cop number fully determined for each variant

Different chess piece moves affect cop number

Game variants on toroidal graphs analyzed

Abstract

We investigate multiple variants of the game Cops and Robbers. Playing it on an $n \times n$ toroidal chess graph, the game is varied by defining moves for cops and robbers differently, always mimicking moves of certain chess pieces. In these cases, the cop number is completely determined.