Transfer-matrix Calculation Of The Independent Set Polynomial And Clar Covering Polynomial

Transfer-matrix method is a useful tool. It mainly applies in the substructure enumeration of graphs which have good recurring structures and the substructure has prescribed properties. The transfer-matrix expressions of the independent set polynomial and the Clar covering polynomial of some graphs are given here. As examples, we show the simple explicit expressions of these two polynomials of several graphs. Consequently, a series of important topological indices such as σ -index(Merrifield-Simmons index), Clar number, the number of Kukule structures, and the first Herndon number are obtained. For unbranched catacondensed hexagonal systems, a general method for determining the independent set polynomial and the Clar covering polynomial is also presented.