On classes of neighborhood resolving sets of a graph

B. Sooryanarayana, Suma A. S.


Let G = (V, E) be a simple connected graph. A subset S of V is called a neighbourhood set of G if G = ⋃s ∈ S < N[s] > , where N[v] denotes the closed neighbourhood of the vertex v in G. Further for each ordered subset S = {s1, s2, ..., sk} of V and a vertex 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) denote the distance between u and v in G. A subset S is said to be resolving set of G if Γ(u/S) ≠ Γ(v/S) for all u, v ∈ V − S. A neighbouring set of G which is also a resolving set for G is called a neighbourhood resolving set (nr-set). The purpose of this paper is to introduce various types of nr-sets and compute minimum cardinality of each set, in possible cases, particularly for paths and cycles.


resolving set, neighbourhood set, neighbourhood resolving sets.

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DOI: http://dx.doi.org/10.5614/ejgta.2018.6.1.3


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ISSN: 2338-2287

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