The forcing polynomial and anti-forcing are two important enumerative polynomials associated with all perfect matchings of a graph. In graph large order, the exhaustive enumeration which is used to compute number given matching too time-consuming number. this paper, we come up an efficient method — integer linear programming, matching. As applications, obtain di-forcing C60 , C70 C72 as consequ...

In recent decades, a number of molecules and diverse dust features have been identified by astronomical observations in various environments. Most of the dust that determines the physical and chemical characteristics of the interstellar medium is formed in the outflows of asymptotic giant branch stars and is further processed when these objects become planetary nebulae. We studied the environme...