The Local Metric Dimension of Some Networks

Let [Formula: see text] be a graph. A set [Formula: see text] is a local resolving set of [Formula: see text] if there exists [Formula: see text] such that [Formula: see text] for any [Formula: see text]. The local metric dimension [Formula: see text] of [Formula: see text] is the minimum cardinality of all the local resolving sets of [Formula: see text]. In this paper, we investigate the local metric dimensions of several typical networks, including antiprism networks, hexagonal ladder networks, radix triangular mesh networks, and sierpiński networks.