Computer Method For Distinguishing Hexagonal System Isopectral Molecules

Isopectral molecules refers to the different graphs those have the same characteristic polynomials. In this paper, the method of computer's simulation is used to make a judgment for isopectral molecules quickly and correctly. Whether hexagonal graphs are isopectral molecules or not is designed by the hexagonal graphs'polynomials. In this paper, the graphs can be quickly and correctly inputted into computer, given every apex a number and graph's adjacency matrix. According to this method, it can distinguish hexagonal system's isopectral molecules we made a test about ten-hexagonal system and find out the isopectral molecules.In this paper, we use Borland C++Builder (BCB) as the interface of the main programs and use Mathematica as copulating the graph's polynomials. Ten-hexagonal system is produced by nine-hexagonal system, each graph has its correspondence polynomial, we put the polynomial into a database and we will obtain a database which contains ten-hexagonal system graph's polynomial, then we retrieve the database to find out the same polynomial. Distinguishing whose structure again further, that is to say, what we find out isopectral molecules.