Non-Isolated Resolving Number of Graphs with Homogeneous Pendant Edges

Abstract

A set is called a resolving set of if every vertices of have diff erent r epr esentation. The minimum cardinalit y 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-isolat ed vert ex. A non-isolat ed resolving number, denoted by , is minimum cardinalit y of non-isolated resolving set in . In this research, we obtain the lower bound of the non isolat ed resolving number of graphs with homogeneous pendant edges,