After introducing and developing fuzzy set theory, a lot of studies have been done in this field and then a result appeared as a Fuzzy Graph (Combination of graph theory and fuzzy set theory). This is now known as Fuzzy graph theory. In this article we review essential works on different types of fuzzy graph and fuzzy hyper graph. Mathematics Subject Classification (2010): 03E72, 05C72

In this research paper, it was studied about degree of vertices of a semitotal blocks in fuzzy graphs. In process we obtain some interesting results regarding the degree of the vertices in semitotal blocks in fuzzy graphs. We observed that when ‘B’ is a block of a given fuzzy graph G:(V, σ, μ), then degree of the vertex B in semi total block fuzzy graph TSTBF(G) is equal to the sum of the membe...

all practical digital circuits are usually a mixture of combinational and sequential logic. flip–flops are essential to sequential logic therefore fuzzy flip–flops are considered to be among the most essential topics of fuzzy digital circuit. the concept of fuzzy digital circuit is among the most interesting applications of fuzzy sets and logic due to the fact that if there has to be an ultimat...

Concepts of graph theory have applications in many areas of computer science including data mining, image segmentation, clustering, image capturing, networks, etc . An interval-valued fuzzy set is a generalization of the notion of a fuzzy set. Interval-valued fuzzy models give more precision, flexibility and compatibility to the system as compared to the fuzzy models. In this paper, we introduc...

in the present paper, we study some properties of fuzzy norm of linear operators. at first the bounded inverse theorem on fuzzy normed linear spaces is investigated. then, we prove hahn banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. finally the set of all compact operators on these spaces is studied.

The concept of fuzzy magic labeling is introduced.Fuzzy magic labeling for some graphs like path, cycle and star graph are defined. It is proved that, every fuzzy magic graph is a fuzzy labeling graph, but the converse is not true. And we show that the removal of a fuzzy bridge from a fuzzy magic graph G, such that G* is a cycle with odd number of nodes is a fuzzy magic graph.And also some prop...