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Rokhana Ayu Solekhah
Universitas Sebelas Maret, Surakarta
Computer Science & IT Decision Sciences, Operations Research & Management

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On the local metric dimension of t-fold wheel, Pn o Km, and generalized fan Rokhana Ayu Solekhah; Tri Atmojo Kusmayadi
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (243.108 KB) | DOI: 10.19184/ijc.2018.2.2.4

Abstract

Let G be a connected graph and let u, v ∈ V(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(v∣W) = (d(v, w1), d(v, w2), ..., d(v, wn)), where d(v, wi) is the distance between v and wi for 1 ≤ i ≤ n. The set W is a local metric set of G if r(u ∣ W) ≠ r(v ∣ W) 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, Pn ⊙ Km graph, and generalized fan graph.
Co-Authors Tri Atmojo Kusmayadi