Vertex connectivity parameters paths and cycles in fuzzy graphs

Abstract

One of the major developments in the 20th century is the evolution of very large newlineinterconnection networks. Even the life of a common man is controlled by several newlinesuch networks. Among different models representing a network, a graph structure is newlinethe most feasible one. In such a model, vertices represent objects and edges represent newlinelinks between them. Designing of a network that is ideal from all perspectives is newlinealmost impossible. Depending on the requirement, a nearly suitable one can be newlinedesigned. When we have a large network, its dynamics can be explained only by its newlinelocal behavior. A comparison of the performances between different regions can be newlinedone only by introducing a fuzzy graph. When there is an uncertainty regarding the newlinecapacities, then also a fuzzy graph model is relevant. newlineAs far as fuzzy graphs are concerned, the concept of connectivity is very crucial, newlineas the real world networks are ideally related to them. The term connectivity can newline newlinebe translated into different terms like maximum bandwidth, maximum width, maxi- newlinemum deliverable speed, bottleneck capacity, etc. based on the type of network we newline newlinediscuss. There are several connectivity parameters, using which one can evaluate the newlineperformance of a network. For example, a higher value for the average bandwidth in newlineinternet network is necessary, for its better performance and stability. newlineThe main objectives of this thesis is to study some of the important connectivity newlineparameters related to a network, represented as a fuzzy graph and to characterize newlinefuzzy graph theoretical structures like fuzzy trees, fuzzy cycles and complete fuzzy newlinegraphs using them. The motivation for this study comes especially from applications newlinerelated to human trafficking and illegal immigration. newline