A study on dominaltion parameters on the products of fuzzy graphs and anit fuzzy graphs

Abstract

A real life problem can be solved by representing the situation as a mathematical newlinemodel. Graph is one of the best suitable ways of representing the relationship between newlineobjects and it is the easiest way to arrive at the solution. In graph, vertices and edges newlinerepresent the objects and their relationship. In some cases, there exist uncertainties in the newlinedescription of the objects or in its relationships or in both which has to be designed as newlinefuzzy graph model. So, fuzzy sets or their precise membership functions provide an newlineinterface between the input and output numerical values. Fuzzy set approaches have newlineseveral advantages over other intelligent modeling technique such as neural networks, newlinecipher-based message authentication code, radial basis function networks. Fuzzy graphs newlinemay be helpful for illustrating delicate or not well characterized structures, for example, newlinein humanistic frameworks. In fuzzy graph, the relation attains only the minimum value newlineamong the objects. Sometimes, if complexity occurs among the relation, then it may lead newlineto obtain maximum values. Such case, the problem is constructed as Anti Fuzzy Graph newlineModel . newline Fuzzy set has exponential growth in research area of mathematics and its newlineapplications such as logic, topology, algebra, analysis. Also it plays very important role in newlinepattern recognition, information theory, artificial intelligence and neural networks, newlinerobotics, signal processing, multi agent systems, decision making etc. [7], [19], [42], newline[116]. A mathematical model to describe the occurrence of uncertainty in real life newlinesituation is first suggested by L. A. Zadeh [114] in 1965. Kaufmann [36] first derived the newlineconcept of fuzzy graph from the fuzzy relation that was introduced by Zadeh [114] in newline1965. In 1975, Rosenfeld [93] introduced another elaborated definition including fuzzy newlinevertex and fuzzy edge. He also proposed the notion of fuzzy graph and several fuzzy newlineanalogs of graph theoretic concepts such as paths, cycles and connectedness. During the newlinesame time.