Journal of Mathematical and Fundamental Sciences (Jun 2021)

Graphs of Neighborhood Metric Dimension Two

  • Badekara Sooryanarayana,
  • Suma Agani Shanmukha

DOI
https://doi.org/10.5614/j.math.fund.sci.2021.53.1.9
Journal volume & issue
Vol. 53, no. 1

Abstract

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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.

Keywords