2008/11/03 by Muhammad Abdullah Adnan, Adnan, Muhammad Abdullah, Masud Hasan +1
Computer Science · Engineering · #Advanced Graph Theory Research #Computational Geometry and Mesh Generation #cs.CG #cs.DM #cs.DS #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.0811.0254
13 pages, 5 figures
arxiv created 2008/11/03 · arxiv updated 2009/12/01
A classic theorem by Steinitz states that a graph G is realizable by a convex polyhedron if and only if G is 3-connected planar. Zonohedra are an important subclass of convex polyhedra having the property that the faces of a zonohedron are parallelograms and are in parallel pairs. In this paper we give characterization of graphs of zonohedra. We also give a linear time algorithm to recognize such a graph. In our quest for finding the algorithm, we prove that in a zonohedron P both the number of zones and the number of faces in each zone is O(square rootn), where n is the number of vertices of P.