2013/09/03 by Dorota Kuziak, Kuziak, D., Juan A. Rodríguez‐Velázquez +3 · 3 citations
Computer Science · #05C12 #05C76 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1309.0641
openalex publication_date 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected graph. Given an ordered set W = \w1, w2,… 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 G. It is well known that the problem of finding the metric dimension of a graph is NP-Hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.