Metric dimension of fullerene graphs
Shehnaz Akhter, Rashid Farooq · Electronic Journal of Graph Theory and Applications · 2019
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.