What are Rook's Graphs? [Discrete Mathematics]

Описание: What is a Rook's graph? A rook's graph is a graph that represents all legal moves of a rook on a chessboard.

A rook's graph's vertices represent squares on a chessboard, and edges represent all possible legal moves a rook can make between 2 squares on a chessboard. Rook's graphs do not have to correspond to a typical 8 x 8 chessboard, instead they can be of any dimensions, and even of rectangular proportions.

A rook's graph is interesting in that it is the cartesian product of two complete graphs. This is one of my favorite graphs because it shows how pure mathematical definitions, can have unexpected and unintended practical applications. In this case, something totally unrelated to chess and unmotivated by chess, like the cartesian product of two complete graphs, can have such a practical application as representing all the legal moves of a rook on a chessboard.

*******************************************************************************************************
If you want to learn more about graph products, I highly recommend the following book:
"Handbook of Product Graphs": https://amzn.to/3HjF5D8

Note: This is my Amazon Affiliate link. As an Amazon Associate I may earn commissions for purchases made through the link above.

#chess
#graphtheory