Metric spaces in chess and international chess pieces graph diameters
Marco Rip\`a

TL;DR
This paper investigates the graph radii and diameters of generalized chess pieces in multi-dimensional lattices, providing exact values for some pieces and bounds for others, thereby extending classical chess metrics into higher dimensions.
Contribution
It introduces a consistent generalization of planar chess pieces to k-dimensional spaces and computes their graph radii and diameters, including exact values and bounds for various pieces.
Findings
Exact graph radii and diameters for k-rook, k-king, k-bishop, 3-queen, 3-knight, 3-pawn.
Tight bounds for k-queen, k-knight, k-pawn for all k ≥ 4.
Extension of chess piece metrics to multi-dimensional lattices.
Abstract
This paper aims to study the graph radii and diameters induced by the -dimensional versions of the well-known six international chess pieces on every finite lattice since they originate as many interesting metric spaces for any proper pair . For this purpose, we finally discuss a mathematically consistent generalization of all the planar FIDE chess pieces to an appropriate -dimensional environment, finding (for any ) the exact values of the graph radii and diameters of the -rook, -king, -bishop, and the corresponding values for the -queen, -knight, and -pawn. We also provide tight bounds for the graph radii and diameters of the -queen, -knight, and -pawn, holding for any .
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Computational Geometry and Mesh Generation
