Abstract
An undirected graph G=(V,E) has metric dimension at most k if there is a vertex set U⊆V such that |U|≤k and ∀u,v∈V, u≠v, there is a vertex w∈U such that dG(w,u)≠dG(w,v), where dG(u,v) is the distance (the length of a shortest path in an unweighted graph) between u and v. The metric dimension of G is the smallest integer k such that G has metric dimension at most k. A cactus block graph is an undirected graph whose biconnected components are either cycles or complete graphs. We present a linear time algorithm for computing the metric dimension of cactus block graphs.
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