Certain Varieties of Resolving Sets of A Graph

Badekara Sooryanarayana, Suma A.S., Chandrakala S.B.

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.

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References


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DOI: https://doi.org/10.22342/jims.27.1.881.103-114

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