The rook's graph (the graph that represents all legal moves of the rook chess piece on a chessboard) is also sometimes called the lattice graph.
In their papers (which are technical) and book (which is for a lay audience, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end.
Graph of a function | graph | Bipartite graph | planar graph | graph theory | Lattice Semiconductor | directed graph | Under Graph | random graph | Planar graph | Graph traversal | Graph theory | Graph (mathematics) | Gabriel graph | visibility graph | Unit distance graph | rook's graph | Rado graph | minor (graph theory) | Lenstra–Lenstra–Lovász lattice basis reduction algorithm | Lattice graph | interval graph | Graph-tool | Graph (data structure) | Graph coloring | graph coloring | Graph | Factor graph | Exponential random graph models | Directed graph |