On the metric dimension of Buckminsterfullerene-net graph

Lyra Yulianti, Des Welyyanti, Yanita Yanita, Muhammad Rafif Fajri, Suhadi Wido Saputro


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 ≤ jk. 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 ≤ tm and m ≥ 2. Let vt be a terminal vertex for each B60t. The Buckminsterfullerene-net, denoted by H:=Amal{B60t,v| 1 ≤ tm; m ≥ 2} is a graph constructed from the identification of all terminal vertices vt, for 1 ≤ tm and m ≥ 2, into a new vertex, denoted by v. This paper will determine the metric dimension of the Buckminsterfullerene-net graph H.


Buckminsterfullerene; amalgamation; Buckminsterfullerene-net; metric dimension

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DOI: http://dx.doi.org/10.19184/ijc.2023.7.2.2


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