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Submitted
October 8, 2019
Accepted
January 25, 2021
Published
March 31, 2021
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Abstract

Let G=(V,E) be a simple connected graph. For each ordered subset S={s_1,s_2,...,s_k} of V and a vertex u in V, we associate a vector Gamma(u/S)=(d(u,s_1),d(u,s_2),...,d(u,s_k)) with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if Gamma(u/S) not equal to Gamma(v/S) for all u, v in V-S. The purpose of this paper is to introduce various types of r-sets and compute minimum cardinality of each set, in possible cases, particulary for paths, cycles, complete graphs and wheels.

Keywords

simple resolving sets metric dimensions landmarks maximal resolving sets null resolving sets.

Article Details

Author Biographies

Badekara Sooryanarayana, Dr. Ambedkar Institute of Technology

Professor of Mathematics

Suma A.S.

Research Scholar

Department of Mathematics

Chandrakala S.B.

Research Scholar

Department of Mathematics

How to Cite
Sooryanarayana, B., A.S., S., & S.B., C. (2021). Certain Varieties of Resolving Sets of A Graph. Journal of the Indonesian Mathematical Society, 27(1), 103–114. https://doi.org/10.22342/jims.27.1.881.103-114
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