模糊图直积中的模糊圈

The Fuzzy Cycle of the Direct Product of Fuzzy Graphs

本文将研究两个模糊图直积中的模糊圈。通过我们的讨论,证明了两个有内点的模糊图的直积中必有模糊圈,而两个无内点的模糊图的直积中必无模糊圈;我们还对直积中所有边是否在某个圈上进行了较为细致的讨论,得到了下列主要结果:任意一个模糊图与模糊圈的直积中必有模糊圈,且每条边均在其某个模糊圈上。

In this paper, we deal with fuzzy cycles of the direct product of fuzzy graphs. With our investigation, it is shown that there exists a fuzzy cycle in the direct product of two fuzzy graphs if each of them has an internal node, and that there is no fuzzy cycle while neither of them has an internal node. Moreover, we also present a detailed investigation over the issue of whether every edge is on a certain cycle, and obtain the following main result: there exists a fuzzy cycle in the direct product with every edge being on a certain fuzzy cycle.