Transitive blocks and their applications in fuzzy interconnection networks

In any network, the problem of reduction of flow is more important and frequent than the disconnection of the network. Problems related with maximum bandwidth paths and maximal flows are also very significant. In this article, the authors discuss connectivity concepts related with paths and flows in interconnection networks in a fuzzy framework. Some of the properties and applications of a stable structure called transitive block are discussed. Blocks in fuzzy graphs generalize the concept of blocks in graphs. The existence of a strongest strong cycle in any fuzzy block having at least three vertices is established. Four characterizations previously proposed for a class of blocks in fuzzy graphs are found to be true for a larger class. Two subclasses of θ-fuzzy graphs, namely, connectivity-transitive and cyclically-transitive fuzzy graphs are introduced to get a better understanding of blocks in fuzzy graphs. An application of transitive blocks in interconnection networks is also proposed.