Cyclic flow is a very crucial concept in most interconnection networks. The cycle connectivity of a network allows one to identify the cyclic flow and hence determine its cyclic reachability. The cycle connectivity of a fuzzy graph depends on the strengths of all strong cycles in the graph. In this paper, we discuss generalized cycle connectivity of fuzzy graphs, which takes into account the strength of all cycles passing through a given pair of vertices of the graph. Generalized cycle connectivity of fuzzy trees, fuzzy cycles, and complete fuzzy graphs are discussed. Generalized cyclic cutvertices and bridges are also studied. Concepts of cyclically stable fuzzy graph are also studied and a condition for a complete fuzzy graph to be cyclically stable is obtained.

中文翻译：

---

模糊图中的广义循环连通性

循环流是大多数互连网络中非常重要的概念。网络的循环连通性允许人们识别循环流，从而确定其循环可达性。模糊图的循环连通性取决于图中所有强循环的强度。在本文中，我们讨论模糊图的广义循环连通性，它考虑了通过图的给定顶点对的所有循环的强度。讨论了模糊树、模糊循环和完全模糊图的广义循环连通性。还研究了广义循环割点和桥。研究了循环稳定模糊图的概念，给出了完全模糊图循环稳定的条件。