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.
出处
《应用数学学报》
CSCD
北大核心
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)
关键词
冠状系统
R-旋转图
有向根树
高度和宽度
coronoid system
R-rotation graph
directed rooted tree
height and width
