Vertex Geodetic Number of a Fuzzy Graph

Abstract

        In this paper, vertex geodetic number of a fuzzy graph is introduced. Let  be a vertex of a connected non-trivial fuzzy graph. A set  of vertices of  is  if each vertex  of lies on   geodesic in  for some element  in. The minimum cardinality of   of  is defined as   of  and is denoted by. A   of cardinality is called  of.