蝶形网络的一般定位问题
General Position Problem of Butterfly Networks
摘要：
一般位置集S是G（V，E）中顶点的集合S，使得S中没有三个顶点位于G中的最短路径上。G中这样一个最大集称为G的gp集，它的势称为G的gp-数，记为gp（G）。介绍一般位置问题的作者指出，蝴蝶网络的一般位置问题是开放的。解决给定网络的一般位置问题的一个众所周知的技术是使用其等距路径覆盖数作为上界。蝴蝶网络的一般位置问题仍然是开放的，因为这种技术不适用于蝴蝶网络。在本文中，我们采用了一种新的技术，使用等距圈覆盖数作为其上界。这种技术是有趣的和有用的，因为它开辟了新的途径来解决网络的一般位置问题，没有解决方案。
英文摘要：
A general position set S is a set S of vertices in G(V,E) such that no three vertices of S lie on a shortest path in G. Such a set of maximum size in G is called a gpset of G and its cardinality is called the gp-number of G denoted by gp(G). The authors who introduced the general position problem stated that the general position problem for butterfly networks was open. A well-known technique to solve the general position problem for a given network is to use its isometric path cover number as an upper bound. The general position problem for butterfly networks remained open because this technique is not applicable for butterfly networks. In this paper, we adopt a new technique which uses the isometric cycle cover number as its upper bound. This technique is interesting and useful because it opens new avenues to solve the general position problem for networks which do not have solutions yet.
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。
