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Determines the adjacency dimension of star-related trees, suggesting valuable insights in graph theory applications.
Locating or resolving sets are introduced as a graph-theoretic model of robot navigation and has different applications in diverse areas like network discovery, computer science and chemistry. These applications leads to some graph parameters, like the metric dimension and the adjacency dimension. A subset S of the vertices of a graph $G$ is an adjacency resolving set for G if for each pair of distinct vertices x, y ∈ V(G) S, there exists s ∈ S which is adjacent to exactly one of these two vertices. An adjacency resolving set with the minimum cardinality is called an adjacency basis and its cardinality is the adjacency dimension of G. Since the problem of computing the adjacency dimension of a graph is NP-hard, finding the adjacency dimension of special classes of graphs or obtaining good bounds on this invariant is valuable. In this paper we determine the adjacency dimension of some famous star related trees.
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Hardani et al. (2026) studied this question.
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