The non-isolated resolving number of k-corona product of graphs

Abstract

Let all graphs be a connected and simple graph. A set W = fw g of veretx set of G, the kvector ordered r(vjW) = (d(x; w 1 ); d(x; w 2 1 ; w 2 ); : : : ; d(x; w )) of is a representation of v with respect to W, for d(x; w) is the distance between the vertices x and w. The set W is called a resolving set for G if di erent vertices of G have distinct representation. The metric dimension is the minimum cardinality of resolving set W, denoted by dim(G). Through analogue, the resolving set W of G is called non-isolated resolving set if there is no 8v 2 W induced by non-isolated vertex. The non-isolated resolving number is the minimum cardinality of non-isolated resolving set W, denoted by nr(G). In our paper, we determine the non isolated resolving number of k-corona product graph. ; w 3 k ; : : : ; w k