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arXiv · 1602.07537

The local metric dimension of the lexicographic product of graphs

G. A. Barragán-Ramírez·A. Estrada-Moreno·Y. Ramírez-Cruz·J. A. Rodríguez-Velázquez
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Abstract

The metric dimension is quite a well-studied graph parameter. Recently, the adjacency dimension and the local metric dimension have been introduced and studied. In this paper, we give a general formula for the local metric dimension of the lexicographic product $G \circ \mathcal{H}$ of a connected graph $G$ of order $n$ and a family $\mathcal{H}$ composed by $n$ graphs. We show that the local metric dimension of $G \circ \mathcal{H}$ can be expressed in terms of the true twin equivalence classes of $G$ and the local adjacency dimension of the graphs in $\mathcal{H}$.

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G. A. Barragán-Ramírez, A. Estrada-Moreno, Y. Ramírez-Cruz, J. A. Rodríguez-Velázquez. 2016-02-24. The local metric dimension of the lexicographic product of graphs. https://arxiv.org/abs/1602.07537

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