# Graphs of Neighborhood Metric Dimension Two

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2021.53.1.9## Keywords:

landmarks, metric dimension, neighborhood metric dimension, neighborhood set## Abstract

A subset of vertices of a simple connected graph is a neighborhood set (*n*-set) of *G* if *G* is the union of subgraphs of *G* induced by the closed neighbors of elements in *S*. Further, a set *S* is a resolving set of *G* if for each pair of distinct vertices *x,y* of *G*, there is a vertex *s?S* such that d(s,x)?d(s,y). An *n*-set that serves as a resolving set for *G* is called an *nr*-set of *G*. The *nr*-set with least cardinality is called an *nr*-metric basis of *G* and its cardinality is called the neighborhood metric dimension of graph *G*. In this paper, we characterize graphs of neighborhood metric dimension two.

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