ON THE METRIC DIMENSION OF BUCKMINSTERFULLERENE-TYPE (B60(1, t)) FOR 1 <= t <= 5
DOI:
https://doi.org/10.25077/jmua.15.4.611-623.2026Keywords:
Dimensi metrik, graf Buckminsterfullerene, graf Buckminsterfullerene-type, himpunan pemisah, representasiAbstract
Let G = (V, E) be a connected graph with vertex set V(G) and edge set E(G). For any two vertices u and v in G, the length of the shortest path between u and v in G is denoted by d(u, v). Let A = {a1, a2, ..., ak} be an ordered set of vertices of a connected graph G, and let v be a vertex in V(G). The representation of vertex v with respect to A, denoted by r(v|A), is defined as r(v|A) = (d(v, a1), d(v, a2), ..., d(v, ak)). If every pair of distinct vertices in G has distinct representations with respect to A, then A is called a resolving set of G. A resolving set with minimum cardinality is called a minimum resolving set, and its cardinality is called the metric dimension of G, denoted by dim(G). In this paper, we discuss the metric dimension of the Buckminsterfullerene-type graph, denoted by B60(1, t), for 1 <= t <= 5. Specifically, the main results reveal that dim(G) = 4 for t = 1 and dim(G) = 2t + 1 for 2 <= t <= 5.
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