MORE RESULTS ON NON-ISOLATED RESOLVING NUMBER OF A GRAPH

Let be a connected graph. Let be a subset of with an order imposed on it. For any , the vector is called the metric representation of with respect to . If distinct vertices in have distinct metric representation, then is called a resolving set of . The minimum cardinality of a resolving set of is called the metric dimension of and it is denoted by . A resolving set is called a non-isolated resolving set if the induced sub graph has no isolated vertices. The minimum cardinality of a non-isolated resolving set of is called the non-isolated resolving number of and is denoted by . In this paper, we determine the non-isolated resolving number for some standard graphs like double broom, the join of complete graphs and paths, etc. Further more, we discuss about the relationship of with other parameters