Indonesian Journal of Combinatorics
Vol 2, No 2 (2018)

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

Solekhah, Rokhana Ayu ( Universitas Sebelas Maret, Surakarta )
Kusmayadi, Tri Atmojo ( Universitas Sebelas Maret, Surakarta )

Article Info

Publish Date
21 Dec 2018


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.

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Journal Info





Computer Science & IT Decision Sciences, Operations Research & Management


Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian ...