On the metric dimension of Buckminsterfullerene-net graph - Yulianti, Lyra; Welyyanti, Des; Yanita, Yanita; Fajri, Muhammad Rafif; Saputro, Suhadi Wido (Indonesian Combinatorial Society (InaCombS), 2023)
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:=AmalB60t,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.