Open AccessGraphs of Neighborhood Metric Dimension Two
Author(s) -
B. Sooryanarayana,
Suma Agani Shanmukha
Publication year - 2021
Publication title -
journal of mathematical and fundamental sciences/journal of mathematical and fundamental siences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.216
H-Index - 12
eISSN - 2337-5760
pISSN - 2338-5510
DOI - 10.5614/j.math.fund.sci.2021.53.1.9
Subject(s) - metric dimension , combinatorics , mathematics , vertex (graph theory) , discrete mathematics , graph , cardinality (data modeling) , metric (unit) , dimension (graph theory) , chordal graph , computer science , 1 planar graph , operations management , economics , data mining
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.