Non-isolated resolving number of graphs with homogeneous pendant edges

Abstract

All graphs in this paper are a simple, nontrivial and connected graph . A set of vertex set of , is a representation of vertex to , the distance between the vertex and the vertex , denoted by . A set is called a resolving set of if every vertices of have different representation. The minimum cardinality of resolving set is metric dimension, denoted by . Furthermore, the resolving set of is called the non-isolated resolving set if there does not for all induced by the non-isolated vertex. A non-isolated resolving number, denoted by , is minimum cardinality of non-isolated resolving set in . In this research, we obtain the lower bound of the non isolated resolving number of graphs with homogeneous pendant edges, for and these results of the non isolated resolving number of graphs with homogeneous pendant edges with with a path , complete graph and cycle .