Anti-Forcing Polynomial Of The Several Classes Of Fullerene Graph

Let G be a finite simple connected graph and M be a perfect matching(called Kekule structure in Chemistry)of G,Sa(?)E(G)\M.If Sa is deleted from G,the perfect matching of G is only M,then Sa is called anti-forcing set of M.The minimum |Sa| is called the anti-forcing number of the perfect matching M of G.The polynomial composed of the number of perfect matching with the same anti-forcing number is the coefficient and the anti-forcing number is the exponent is called the anti-forcing polynomial.In this paper,we calculate the anti-forcing numbers of some fullerenes by using the method of integer linear programming,and give their anti-forcing polynomials.This paper is divided into five chapters.In Chapter 1,we introduce the research background and current situation of matching forcing and anti-forcing,as well as some concepts,terms and notations we need to use.The Chapter 2,we introduce the calculative method of this paper.The first is exhaustive method.Later,it is found that this method is not feasible for large graphs.So a new method,integer linear programming method,is introduced,and the specific idea of calculating the anti forcing number is described.In Chapter 3,we give the some calculative results of C60.The relationship of between the perfect matchings of C60 and Hamilton cycles and Hamilton cycles is discussed.The number of alternating cycles of every perfect matching of C60 is calculated.Then anti-forcings number is calculated by integer linear programming,and the anti-forcing polynomial is given.In Chapter 4 and 5,we introduce briefly C70 and some fullerene graphs which their numbers of vertice,and calculate their anti-forcing polynomial.