AN APPLICATION OF Gd -METRIC SPACES AND METRIC DIMENSION OF GRAPHS

The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found applications in optimization, navigation, network theory, image processing, pattern recognition etc. Several other authors have studied metric dimension of various standard graphs. In this paper we introduce a real valued function called generalized metric → + Gd : X × X × X R where X = r(v /W) = {(d(v,v1 ),d(v,v2 ),...,d(v,vk /) v∈V (G))}, denoted Gd and is used to study metric dimension of graphs. It has been proved that metric dimension of any connected finite simple graph remains constant if Gd numbers of pendant edges are added to the non-basis vertices