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All Journal Indonesian Journal of Combinatorics
Muhammad Rafif Fajri
Department of Mathematics, Andalas University Kampus UNAND Limau Manis Padang 25163, Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management

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On the metric dimension of Buckminsterfullerene-net graph Lyra Yulianti; Des Welyyanti; Yanita Yanita; Muhammad Rafif Fajri; Suhadi Wido Saputro
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.2

Abstract

The metric dimension of an arbitrary connected graph G, denoted by dim(G), is the minimum cardinality of the resolving set W of G. An ordered set W = {w1, w2,..., wk} is a resolving set of G if for all two different vertices in G, their metric representations are different with respect to W. The metric representation of a vertex v with respect to W is defined as k-tuple r(v|W) = (d(v,w1), d(v,w2),..., d(v,wk)), where d(v,wj) is the distance between v and wj for 1 ≤ j ≤ k. The Buckminsterfullerene graph is a 3-reguler graph on 60 vertices containing some cycles C5 and C6. Let B60t denotes the tth  B60 for 1 ≤ t ≤ m and m ≥ 2. Let vt be a terminal vertex for each B60t. The Buckminsterfullerene-net, denoted by H:=Amal{B60t,v| 1 ≤ t ≤ m; m ≥ 2} is a graph constructed from the identification of all terminal vertices vt, for 1 ≤ t ≤ m and m ≥ 2, into a new vertex, denoted by v. This paper will determine the metric dimension of the Buckminsterfullerene-net graph H.
Co-Authors Des Welyyanti Suhadi Wido Saputro Yanita Yanita Yulianti, Lyra