类循环图的可定向嵌入  

Genus Polynomials of a Circular-like Graph

作　　者：才仁文毛 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《应用数学学报》2015年第3期460-465,共6页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11371052)资助项目

摘　　要：陈仪朝等运用覆盖矩阵和Chebyshev多项式计算了一些图类在曲面上的亏格分布,本文给出了一类不能运用Chebyshev多项式的类循环图,计算出它在可定向曲面上的嵌入.A surface is a compact connected orientable 2-manifold which could be thought of as a sphere on which has been placed a number of handles. The number of handles is referred to as the genus of the surface. By an embedding of a graph G on a surface S if G is drawn on S so that edges of G intersect only at their common end vertices. The genus distributions of graphs began with J. Gross et al. in 1980s, it could be shown by genus polynomials. Chen Yichao et al. found a new usage of Chebyshev polynomials, by using the overlap matrix and Chebyshev polynomials of the second kind, they obtained homogeneous recurrence ralation for rank distribution polynomial. The embedding distribution of ringle ladders, star-ladders and circular ladders have been calculated. But for some graphs, this method can not be used, in this paper, we get the genus polynomials of a circular-like Graph on orientable surface which can not use Chebyshev polynomiMs.

关 键 词：类循环图 可定向曲面嵌入 

分 类 号：O157.5[理学—数学]