Abstract
A directed Cayley graph C(Γ, X) is specified by a group Γ and an identity-free generating set X for this group. Vertices of C(Γ, X) are elements of Γ and there is a directed edge from the vertex u to the vertex v in C(Γ, X) if and only if there is a generator x ∈ X such that ux = v. We study graphs C(Γ, X) for the direct product Zm × Zn of two cyclic groups Zm and Zn, and the generating set X = {(0, 1), (1, 0), (2, 0), …, (p, 0)}. We present resolving sets which yield upper bounds on the metric dimension of these graphs for p = 2 and 3.
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The work of T. Vetrík has been supported by the National Research Foundation of South Africa; grant numbers: 90793, 112122.
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Mengesha, D.A., Vetrík, T. Resolving Sets of Directed Cayley Graphs for the Direct Product of Cyclic Groups. Czech Math J 69, 621–636 (2019). https://doi.org/10.21136/CMJ.2019.0127-17
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DOI: https://doi.org/10.21136/CMJ.2019.0127-17