论文标题
签名的图形和签名的高度二十面体组的周期
Signed Graphs and Signed Cycles of Hyperoctahedral Groups
论文作者
论文摘要
对于带有边订单的图形，边缘集合的线性顺序，我们通过将边缘视为端换剂的换位来获得顶点的排列。从Dénes的结果中知道，树的置换是任何边缘排序的完整循环。作为推论，Dénes通过最小数量的转置数量的乘积来计算完整循环置换的表示数。此外，带有边排序的图形是完整循环的，以图形嵌入为特征。 在本文中，我们考虑了这些结果的类比，用于签名的图和高二十六角形群体。我们给出了具有符号图的必要条件，可以具有边缘排序，以使排列是一个均匀（或奇数）的全循环。我们表明，带有一些循环的符号树的边缘排序总是给出均匀（或奇数）的完整循环置换，并通过最小数量的换位数量的乘积来计算奇数完整循环置换的表示数。
For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices. It is known from Dénes' results that the permutation of a tree is a full cyclic for any edge ordering. As a corollary, Dénes counted up the number of representations of a full cyclic permutation by means of product of the minimal number of transpositions. Moreover, a graph with an edge ordering which the permutation is a full cyclic is characterized by graph embedding. In this article, we consider an analogy of these results for signed graphs and hyperoctahedral groups. We give a necessary and sufficient condition for a signed graph to have an edge ordering such that the permutation is an even (or odd) full cyclic. We show that the edge ordering of the signed tree with some loops always gives an even (or odd) full cyclic permutation and count up the number of representations of an odd full cyclic permutation by means of product of the minimal number of transpositions.
