In this paper the authors give an O(n2) algorithm to determine fixed bonds and normal subhexagonal systems in a hexagonal system. By this algorithm they can decompose a hexagonal system into a number of regions consisting of fixed bonds and a number of normal subhexagonal systems. This decomposition can be used to simplify the procedure of finding Clar’s formula, counting the number of Kekulé structures and constructing the Z-transformation graph of a hexagonal system with fixed bonds, especially for large hexagonal systems. The authors also give characterizations of hexagonal systems with fixed single and double bonds, respectively.
