Clar and Sextet Polynomials of BN-Fullerenes and BN-Nanotubes

Clarsextet理论因其在比较分子稳定性和计算共振能中的作用而广受关注。ShiuWC等人计算了$C_{60}$的$Clar$结构的数量并给出其$Clar$多项式和$sextet$多项式，而对于硼氮富勒烯，相应的问题尚未解决。本文的研究对象包括由SeifertG等人确定的相对较稳定的3种硼氮富勒烯（$B_{12}N_{12}$，$B_{16}N_{16}$和$B_{28}N_{28}$）以及带帽的硼氮纳米管。本文主要结论如下：1.第二章和第三章利用六边形对偶图的性质研究了$B_{12}N_{12}$和$B_{16}N_{16}$的结构，通过组合计数的方法给出了二者的$Clar$多项式和$se...Clar sextet theory is well known for its role in research of molecule stability and resonance energy. Shiu W C et al. computed the count of Clar structures of$C_{60}$and the associated Clar polynomial and sextet polynomial. For boron-nitrogen fullerenes, the corresponding problem has not been solved. This paper considers three BN-fullerenes ($B_{12}N_{12}$,$B_{16}N_{16}$and$B_{28}N_{28}$) whic...学位：理学硕士院系专业：数学系_应用数学学号：20022304

Clar and Sextet Polynomials of Boron2nitrogen Fullerenes

摘要: Clar 结构因其在比较分子稳定性中的作用而广受关注. Shiu W C 等人计算了C60的Clar 结构的数量并给出其Clar 多项式和sextet 多项式,而对于硼氮富勒烯,相应的问题尚未解决. 本文考查了Seifert G等人确定的最稳定的3 种硼氮富 勒烯的结构特征,通过组合原理得到B12 N12 ,B16 N16 的Clar 多项式和Sextet 多项式,并给出了详细证明. 此外还给出用于 一般硼氮富勒烯的计算程序,并作为例子给出B28N28的Clar 多项式和Sextet 多项式. 本文的结果解决了一般的硼氮富勒 烯分子Clar 多项式和Sextet 多项式的计算工作. Abstract : Shiu W C et al. computed the count of Clar st ructures of C60 and the associated Clar polynomial and sextet polynomial. For boron2nit rogen fullerenes ,the corresponding problem has not been solved. This paper considers three BN2fullerenes which were a2 nomalously stable. By combinatorial techniques the Clar polynomial and the sextet polynomial of B12N12 and B16N16 are given. Detailed proof is also provided. Furthermore ,a program for general cases is designed. As an illust ration ,the Clar polynomial and the sextet pol2 ynomial of B28N28 is given.国家自然科学基金(10371102) 资

Clar and Sextet Polynomials of Boron-nitrogen Fullerenes

Clar结构因其在比较分子稳定性中的作用而广受关注.Shiu W C等人计算了C60的Clar结构的数量并给出其Clar多项式和sextet多项式,而对于硼氮富勒烯,相应的问题尚未解决.本文考查了Seifert G等人确定的最稳定的3种硼氮富勒烯的结构特征,通过组合原理得到 B12 N12,B16 N16的 Clar多项式和 Sextet多项式,并给出了详细证明.此外还给出用于一般硼氮富勒烯的计算程序,并作为例子给出B28N28的Clar多项式和Sextet多项式.本文的结果解决了一般的硼氮富勒烯分子Clar多项式和Sextet多项式的计算工作.Shiu W C et al.computed the count of Clar structures of C_(60) and the associated Clar polynomial and sextet polynomial.For boron-nitrogen fullerenes,the corresponding problem has not been solved.This paper considers three BN-fullerenes which were anomalously stable.By combinatorial techniques the Clar polynomial and the sextet polynomial of B_(12)N_(12) and B_(16)N_(16) are given.Detailed proof is also provided.Furthermore,a program for general cases is designed.As an illustration,the Clar polynomial and the sextet polynomial of B_(28)N_(28) is given.国家自然科学基金(10371102)资