Bidiakis cube theorem, it is a 3-vertex-connected simple planar graph. The Bidiakis cube is not a vertex-transitive graph and its full automorphism group is isomorphic to the dihedral group of order 8, the group of symmetries of a square, including both rotations and reflections. The characteristic polynomial of the Bidiakis cube is formula_1. Bidiakis cube In the mathematical field of graph theory, the Bidiakis cube is a 3-regular graph with 12 vertices and 18 edges. The Bidiakis cube is a cubic Hamiltonian graph and can be defined by the LCF notation [-6,4,-4]. The Bidiakis cube can also be constructed from a cube
Klee–Minty cube visits all corners of a (perturbed) cube in dimension "D" in the worst case. Modifications of the Klee–Minty construction showed similar exponential time complexity for other pivoting rules of simplex type, which maintain primal feasibility, such as Bland's rule. Another modification showed that the criss-cross algorithm, which does not maintain primal feasibility, also visits all the corners of a modified Klee–Minty cube. Like the simplex algorithm, the criss-cross algorithm visits all 8 corners of the three-dimensional cube in the worst case. Further modifications of the Klee–Minty cube have shown poor performance of central-path–following algorithms for linear optimization, in that the