Di-Forcing Polynomials For Ladder Graphs And Fullerene Graphs Of Order Less Than 60

In this paper,by discussing and counting the matching cases of the associated edges of a given vertex,we get the recursion formula of the di-forcing polynomial of the ladder graph.And by using the integer linear programming method with the soft Mathematica,we obtain the di-forcing polynomial of all 3958 isomers of fullerene graphs of order less than 60 and some summary conclusions.In Chapter 1,we mainly introduce some related basic symbols,terms as well as some basic concepts and the main conclusions of this paper.In Chapter 2,we get the recursion formula of the di-forcing polynomials of the ladder graph by classification discussion and counting the matching cases of the associated edges of a given vertex.Basing on this result,we calculate the generating function of di-forcing polynomials of a ladder graph and list the di-forcing polynomials for a few ladder graphs with lower orders.In Chapter 3,we use the relatively efficient integer linear programming method to calculate the matching forcing spectrua and anti-forcing spectrua for all 3958 isomers of fullerene graphs of order less than 60.Their continuities are given accordingly,and the corresponding results are summarized into a series of tables.In Chapter 4,we obtain some extremal aspect related to the stability of fullerene graphs of order less than 60,and draw some conclusions by summarizing them.