On the local metric dimension of t-fold wheel, Pn o Km, and generalized fan

Rokhana Ayu Solekhah, Tri Atmojo Kusmayadi

Abstract


Let G be a connected graph and let u, vV(G). For an ordered set W = {w1, w2, ..., wn} of n distinct vertices in G, the representation of a vertex v of G with respect to W is the n-vector r(vW) = (d(v, w1), d(v, w2), ..., d(v, wn)), where d(v, wi) is the distance between v and wi for 1 ≤ in. The set W is a local metric set of G if r(uW) ≠ r(vW) for every pair u, v of adjacent vertices of G. The local metric set of G with minimum cardinality is called a local metric basis for G and its cardinality is called a local metric dimension, denoted by lmd(G). In this paper we determine the local metric dimension of a t-fold wheel graph, PnKm graph, and generalized fan graph.


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DOI: http://dx.doi.org/10.19184/ijc.2018.2.2.4

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