Forcing bonds of a benzenoid system

Abstract

For a Kekulean benzenoid system, we can define the fixed single bonds, fixed double bonds and forcing bounds. The first and second types of bonds can be recognized by efficient algorithms. In this paper, we give an efficient algorithm to recognize the forcing bonds of a benzenoid system. For a cata-condensed benzenoid system we completely determine its forcing bonds. Furthermore, by Polya's theorem we enumerate all cata-condensed benzenoid Systems with forcing bonds.