None of the coronoid systems can be isometrically embedded into a hypercube ?
A graph that can be isometrically embedded into a hypercube is called a partial cube (or binary Hamming graph). Klavar, Gutman and Mohar [S. Klavar, I. Gutman, B. Mohar, Labeling of benzenoid systems which reflects the vertex-distance relations, J. Chem. Inf. Comput. Sci. 35 (1995) 590593] showed that all benzenoid systems are partial cubes. In this article we show that none of the coronoid systems (benzenoid systems with holes) is a partial cube.
coronoid system isometric embedding hypercube partial cube benzenoid system wiener index