µ- Geodetic Iteration Number and µ- Geodetic Number of a Fuzzy Graph

In this paper the concepts of µ−geodesic, µ−eccentricity, µ−radius, µ−diameter, µ−center, µ−geodetic closure, µ−geodetic iteration number are introduced. It is proved that if G : (V, σ, µ) is a connected fuzzy graph on n nodes such that each pair of nodes is joined by a strong arc then the µ−distance between two nodes is the reciprocal of its arc length. Also the concepts of µ−convex set, µ−geodetic cover, µ−geodetic basis, µ−geodetic number, µ−check node, µ−convex hull, µ−hull number are introduced. A sufficient condition for a fuzzy graph to have its node set as µ−geodetic basis is obtained. µ−peripheral vertex, µ−peripheral path and µ−eccentric vertex of fuzzy graph are analyzed.