Research into the Group of Two-dimensional Magic Cube and its Cayley Graph Diameter

Abstract

Based on the rules of magic cubes, a game of two-dimensional magic cube was deliberately designed. This essay will explore its properties with the assistance of group theory and computer programming. It will first elaborate the rules of two-dimensional magic cube and then use group theory to comprehensively study its properties like the order of the permutation group of the cube, the diameter of Cayley Graph, etc. At the last part of the paper, a much more general result will be raised to satisfy situations like the irregular magic cubes.