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Abstract

Let G = (V, E) be a simple connected graph and S = {s1,s2,…, sk} be an ordered subset of V. Then for u∈ V, we associate a vector Γ(u/S) = (d(u/s1),d(u/s2),…,d(u/sk)) with respect to S, where d(u/v)= (Σui∈N[u] d(ui/v))/(deg(u)+1). A subset S is said to be rational resolving set if Γ(u/S) ̸= Γ(v/S) for all u,v∈ V-S. The minimum cardinality of a rational resolving set S is called rational metric dimension and denoted by rmd(G). A rational resolving set S with minimum cardinality is called rational metric basis. In this paper, we compute rational metric dimension of standard graphs and hence show that rational metric basis serves the same purpose of metric basis with fewer vertices than in any classes of metric basis.

How to Cite this Article:

A. Raghavendra, B. Sooryanarayana, C. Hegde, Rational metric dimension of graphs, Communications in Optimization Theory 2014 (2014), Article ID 8.