Anti-Forcing Polynomials Of Several Special Graphs

In this paper,the perfect matchings of the graphs are classfied according to the situation that contains a certain vertex associated edge.The recurrence relations of partial anti-forcing polynomials of some basic graphs are respectively calculat-ed.Then the partial anti-forced polynomials of each type of perfect matchings are obtained.Finally,by adding all kinds of perfect matchings partial anti-forcing polynomials to get the anti-forcing polynomial of this graph.The first chapter,we briefly introduce the research background and achieve-ments of lattice graphs and hexagonal systems,and give the basic concepts,theo-rems,lemmas,and the basic concepts and properties of the anti-forcing polynomials and partial anti-forcing polynomials of graphs.The second chapter,we first introduces the definition of "X" type ladder graph and its degradation "T" type ladder graph.Secondly,the perfect matching of "X"type ladder graph is classified according to its structural characteristics.Further-more,the anti-forcing polynomials of various situations are further decomposed into the sum of the anti-forcing polynomials of several ladder graphs.Then,the anti-forcing polynomials for every kind of perfect matching are obtained by means of the partial and complete anti-forcing polynomials of the ladder graph.Thus,the anti-forcing polynomials of "X" type ladder graph and the "T" type ladder graph are obtained.Finally,the relationship between the perfect matching number of some special ladder graphs and Fibonacci number related sequences is also given.The third chapter,we give some anti-forcing polynomials of special cata-condenced hexagonal systems.The anti-forcing polynomial of the crown chain G₂ obtained by connecting two crown hexagonal system units.The anti-force polynomial of the hexagonal system in which the crown hexagonal system unit connects multiple lin-ear hexagonal chains of equal length.The fourth chapter,we study anti-forcing polynomials of several special even polygon systems by connecting linear hexagonal chains and ladder graphs.The anti-forcing polynomials of the special even polygon system which is obtained by the coronal hexagonal system element connecting multiple equal-length ladder graphs.