Metric dimension of fullerene graphs

Shehnaz Akhter (School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan)
Rashid Farooq (School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad,)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 1 (2019): Electronic Journal of Graph Theory and Applications

A resolving set W is a set of vertices of a graph G(V, E) such that for every pair of distinct vertices u, v ∈ V(G), there exists a vertex w ∈ W satisfying d(u, w) ≠ d(v, w). A resolving set with minimum number of vertices is called metric basis of G. The metric dimension of G, denoted by dim(G), is the minimum cardinality of a resolving set of G. In this paper, we consider (3, 6)-fullerene and (4, 6)-fullerene graphs and compute the metric dimension for these fullerene graphs. We also give conjecture on the metric dimension of (3, 6)-fullerene and (4, 6)-fullerene graphs.