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Article overview
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On the (adjacency) metric dimension of corona and strong product graphs and their local variants: combinatorial and computational results | | Juan A. Rodríguez-Velázquez
; Henning Fernau
; | | Date: |
9 Sep 2013 | | Abstract: | The metric dimension is quite a well-studied graph parameter. Recently, the
adjacency metric dimension and the local metric dimension have been introduced.
We combine these variants and introduce the local adjacency metric dimension.
We show that the (local) metric dimension of the corona product of a graph of
order $n$ and some non-trivial graph $H$ equals $n$ times the (local) adjacency
metric dimension of $H$. This strong relation also enables us to infer
computational hardness results for computing the (local) metric dimension,
based on according hardness results for (local) adjacency metric dimension that
we also provide. We also study combinatorial properties of the strong product
of graphs and emphasize the role different types of twins play in determining
in particular the adjacency metric dimension of a graph. | | Source: | arXiv, 1309.2275 | | Services: | Forum | Review | PDF | Favorites | |
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