---
tag: RZTXV8FF4A
kind: concept
name: Rook's graph
aliases: [rook-graph]
sources:
  - wikipedia: en:7324959@r1356336964
    locator: Rook's graph
    note: adopted
    mention: wikipedia://en/7324959
    sections: [Summary]
same_as:
  wikidata: Q7366184
  wikipedia: Rook's graph
inventory: [567N6QXJMM]
---

## Summary

In graph theory, a **rook's graph** is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and there is an edge between any two squares sharing a row (rank) or column (file), the squares that a rook can move between. These graphs can be constructed for chessboards of any rectangular shape. Although rook's graphs have only minor significance in chess lore, they are more important in the abstract mathematics of graphs through their alternative constructions: rook's graphs are the Cartesian product of two [[complete graphs|03WKB2H474]], and are the line graphs of [[complete bipartite graphs|0V0GC7BQAN]]. The square rook's graphs constitute the two-dimensional Hamming graphs.