Abstract
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.
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