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Simultaneous resolvability in graph families. (English) Zbl 1338.05223

Rodríguez Velázques, Juan Alberto (ed.) et al., Extended abstracts of the IX “Jornadas de matemática discreta y algorítmica” (JMDA), Tarragona, Spain, July 7–9, 2014. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 46, 241-248, electronic only (2014).
Summary: A set \(S \subseteq V\) is said to be a simultaneous metric generator for a graph family \(\mathcal{G} = \{G_1, G_2, \ldots, G_k\}\), defined on a common vertex set, if it is a generator for every graph of the family. A minimum simultaneous metric generator is called a simultaneous metric basis, and its cardinality the simultaneous metric dimension of \(\mathcal{G}\). We study the properties of simultaneous metric generators and simultaneous metric bases, and calculate closed formulae or tight bounds for the simultaneous metric dimension of several graph families.
For the entire collection see [Zbl 1297.05006].

MSC:

05C75 Structural characterization of families of graphs
05C12 Distance in graphs
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References:

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