Bidiakis cube 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 by adding edges across the top and bottom faces which connect the centres of opposite sides of the faces. The two additional edges need to be perpendicular to each other. With this construction, the Bidiakis cube is a polyhedral graph, and can be realized as a convex polyhedron. Therefore, by Steinitz's
Folded cube graph nearly the same vertex degree but only half the diameter. Efficient distributed algorithms (relative to those for a "hypercube") are known for broadcasting information in a folded cube. Folded cube graph In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects "opposite" pairs of hypercube vertices. The folded cube graph of order "k" (containing 2 vertices) may be formed by adding edges between opposite pairs of vertices in a hypercube graph of order "k" − 1. (In a hypercube with 2 vertices, a pair of