冠状系统的R-旋转图与-旋转图  

The Relation beteen the R-rotation Graph and the-rotation Graph of a Coronoid System

作　　者：祁忠斌[1] 张和平[2] 

机构地区：[1]兰州工业高等专科学校基础学科部,兰州730050 [2]兰州大学数学与统计学院,兰州730000

出　　处：《应用数学学报》2010年第2期269-280,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10831001);甘肃省教育厅科研资助项目(0712B-02)

摘　　要：冠状系统H^c的R()-旋转变换是指对H^c的一个完美匹配M,同时将H^c中所有正常(非正常)M-交错的六边形变换为非正常(正常)M-交错的六边形,从而得到H^c的另一个完美匹配的变换.通过这两种旋转变换可分别建立H^c完美匹配集上的层次结构,分别称为R-旋转图和-旋转图,记为R(H^c)和(H^c).已经证明知道R(H^c)是有向森林,其每个分支都为有向根树.首先讨论了冠状系统的Z-变换有向图与其R-旋转图之间的关系,指出按连通分支对这两种图的顶点集进行划分,其结果一样.在此基础上,证明了R(H^c)的任一分支T(有向根树)都对应(H^c)的一个分支T,且两者的顶点集相同,进而证明了T与T具有相同的高度和宽度.The R-rotational transformation of a coronoid system Hc is a transformation that transforms simultaneously all proper M-alternating hexagons of Hc into improper M-alternating hexagons for a perfect matching M of Hc,and so changes M to another perfect matching.By these two rotational transformations,two hierarchical structures can be generated,which are called R-rotation graph and-rotation graph and denoted by R（Hc） and（Hc）,respectively.It has been proven that R（Hc）is a directed forest,of which each component is a directed rooted tree.First,the relation between Z-transformation directed graph and R-rotation graph of a coronoid system is discussed,and it is shown that the partitions of vertex-sets of these two graphs according to connected components are the same.Based on the result,it is proven that any component T（directed rooted tree）of R（Hc）is corresponding to a component Tof （Hc）,and both T and T have the same vertex-sets,widths and heights.

关 键 词：冠状系统 R-旋转图 有向根树 高度和宽度 

分 类 号：O157.6[理学—数学]