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Some Classes of Bipartite Graphs Induced by Gray Codes

机译:格雷码归纳的几类二部图

摘要

A Gray code of length n is a list of all binary words of length n such that each two successive codewords differ in only one bit position. If the first and the last codewords also share this property, the Gray code is called cyclic, otherwise it is called non-cyclic. The numbers indicating bit positions in where two successive codewords differ in the list of Gray codes are called transition numbers, and the sequence of these all numbers is called the transition sequence of the Gray code. In this article, bit positions of a Gray code of length n will be counted from 1 up until n. If a graph with vertex set {1, 2, ..., n} having the property that two vertices i and j are adjacent in the graph if and only if, i and j are consecutive transitions in the transition sequence of a Gray code, then the graph is called induced by the Gray code. Some classes of bipartite graphs are shown to be induced by Gray codes. Particularly, we show that complete bipartite graphs are induced by Gray codes.
机译:长度为n的格雷码是长度为n的所有二进制字的列表,以使得每两个连续的码字仅在一个比特位置上有所不同。如果第一个和最后一个码字也共享此属性,则格雷码称为循环码,否则称为非循环码。表示格雷码列表中两个连续码字不同的位的位置的数字称为过渡编号,所有这些数字的序列称为格雷码的过渡序列。在本文中,长度为n的格雷码的位位置将从1开始一直计数到n。如果具有顶点集{1,2,...,n}的图具有以下性质:当且仅当i和j是格雷码的转换序列中的连续转换时,两个顶点i和j在图中相邻,则该图被格雷码归纳。某些类别的二部图显示为由格雷码引起。特别是,我们显示了完整的二部图是由格雷码引起的。

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  • 作者

    Suparta, I Nengah;

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  • 年度 2017
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  • 原文格式 PDF
  • 正文语种 EN
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