### Metric dimension of fullerene graphs

#### Abstract

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.

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#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2019.7.1.7

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