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Suma Agani Shanmukha
Department of Mathematics, School of Applied Sciences, REVA University, Yelahanka, Bengaluru, Karnataka State, India, Pin 560 064.
Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

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Graphs of Neighborhood Metric Dimension Two Badekara Sooryanarayana; Suma Agani Shanmukha
Journal of Mathematical and Fundamental Sciences Vol. 53 No. 1 (2021)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2021.53.1.9

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.
Co-Authors Badekara Sooryanarayana