A study on connectivity parameters of networks using fuzzy graph theory and#8195;

Abstract

The visualization of architecture of networks is possible only by means of newlinegraphs, in which vertices symbolize nodes and edges symbolize links between newlinenodes. It is almost infeasible to build up a design of a network that is favorable newline newlinefrom all aspects. A suitable network has to be designed depending on the re- newlinequirements of the and#57346;eld. The main objective of this thesis is to propose some of newline newlinethe important connectivity parameters related to a network by modeling it as a newline newlinefuzzy graph and characterize diand#57345;erent types of structures using them. Connec- newlinetivity index and average connectivity index, which are proposed in this work, are newline newlineindicators of and#57347;ow within a network. Wiener index provides a kind of distance newlinenotion whereas cyclic connectivity index and average cyclic connectivity index newlineprovide measures of cyclic reachability of the network. We provide algorithms to newlinecalculate these parameters. Also algorithms are developed to improve the values newline newlineof these parameters and hence to enhance the reliability of the network, if possi- newlineble. While designing the network topology, these parameters assure a minimum newline newlinestatic and#57347;ow and help to keep the network stable and dynamic. In order to reduce newlinethe cost or power consumption, if the network manager is forced to reduce the newlinenumber of nodes in an interconnection network, he can rely on certain neutral newlinenodes. Because, idleness of these kind of vertices will not reduce the average newlineconnectivity index and hence the and#57347;ow in that network can be kept stable. newline