Displaying similar documents to “Stability of graphs.”

Computing the Metric Dimension of a Graph from Primary Subgraphs

Dorota Kuziak, Juan A. Rodríguez-Velázquez, Ismael G. Yero (2017)

Discussiones Mathematicae Graph Theory

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Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . . , d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of...