On Different Types of Geodesic Numbers in Fuzzy Graphs

An attempt is carried out in this book to introduce different types of geodesic numbers in fuzzy graphs including their edge version such as edge geodesic number, pseudo geodesic number, pseudo edge geodesic number, forcing geodesic number, forcing edge geodesic number, connected geodesic number, forcing connected geodesic number, connected edge geodesic number and forcing connected edge geodesic number of fuzzy graphs. These different types of geodesic numbers are determined for some standard fuzzy graphs such as complete fuzzy graphs, fuzzy trees, fuzzy cycles and complete bipartite fuzzy graphs. The concept of g-contour nodes in fuzzy graphs is introduced and the geodesic iteration number of g-contour nodes in fuzzy graphs is obtained. An application of geodesic iteration number of g-contour nodes for determining the central persons in the land-line telecommunication network (LTN) is demonstrated, by means of which churning in the land-line telecommunication system can be reduced by providing a step-wise method for canvassing each and every customer in the network.