AN APPLICATION OF Gd-METRIC SPACES AND METRIC DIMENSION OF GRAPHS
نویسنده
چکیده
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 + → × × R X X X Gd : where = = ) / ( W v r X ( ) { } ) ( / ) , ( ),..., , ( ), , ( 2 1 G V v v v d v v d v v d k ∈ , denoted d G 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 d G numbers of pendant edges are added to the non-basis vertices.
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