# Graphs of Neighborhood Metric Dimension Two

## Authors

• Badekara Sooryanarayana Department of Mathematical and Computational Studies, Dr. Ambedkar Institute of Technology, Bengaluru, Karnataka State, India, Pin 560 056.
• Suma Agani Shanmukha Department of Mathematics, School of Applied Sciences, REVA University, Yelahanka, Bengaluru, Karnataka State, India, Pin 560 064.

## 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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