扭立方体中两个边不交Hamilton圈和两个等结点不交圈的构造
Constructing Two Edge-Disjoint Hamiltonian Cycles and Two Equal Node-Disjoint Cycles in Twisted Cubes
摘要：
超立方体网络结构简单，易于实现，是目前最流行的互连网络之一。$n$维扭曲立方体（记作$TQ_n$）是超立方体的一个重要变体，它具有一些优于超立方体的性质.最近，研究了$TQ_n$的一些有趣的性质。本文对任意奇数$n\geqslant 5$构造了$TQ_n$中两个边不相交的Hamilton圈.两个边不相交的哈密尔顿循环的存在提供了一个优势，当实现两个算法，需要一个环结构，允许消息流量均匀地分布在扭曲的立方体。进一步，对任意奇数$n\geqslant 3$，我们构造了$TQ_n$中两个相等的节点不相交圈，其中两个圈包含相同数目的节点，并且每个节点在一个圈中只出现一次.换句话说，我们将扭曲立方体分解成两个具有相同大小的分量，使得每个分量包含一个Hamilton圈。
英文摘要：
The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. The $n$-dimensional twisted cube, denoted by $TQ_n$, an important variation of the hypercube, possesses some properties superior to the hypercube. Recently, some interesting properties of $TQ_n$ were investigated. In this paper, we construct two edge-disjoint Hamiltonian cycles in $TQ_n$ for any odd integer $n\geqslant 5$. The presence of two edge-disjoint Hamiltonian cycles provides an advantage when implementing two algorithms that require a ring structure by allowing message traffic to be spread evenly across the twisted cube. Furthermore, we construct two equal node-disjoint cycles in $TQ_n$ for any odd integer $n\geqslant 3$, in which these two cycles contain the same number of nodes and every node appears in one cycle exactly once. In other words, we decompose a twisted cube into two components with the same size such that each component contains a Hamiltonian cycle.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
