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
Folded cube graph as many vertices, by identifying together (or contracting) every opposite pair of vertices. An order-"k" folded cube graph is "k"-regular with 2 vertices and 2"k" edges. The chromatic number of the order-"k" folded cube graph is two when "k" is even (that is, in this case, the graph is bipartite) and four when "k" is odd. The odd girth of a folded cube of odd order is "k", so for odd "k" greater than three the folded cube graphs provide a class of triangle-free graphs with chromatic number four and arbitrarily large odd girth. As a distance-regular graph with odd