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

Abstract

Let all graphs be a connected and simple graph. A set W = {w1;w2;w3; ⋯wk} of veretx set of G, the κ-vector ordered r(v|W) = (d(x;w1); d(x;w2); ⋯ d(x;wk)) 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 different 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 ∈ 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.