A Note on Exact n-Step Domination
نویسنده
چکیده
We generalize to n steps the notion of exact 2-step domination introduced by Chartrand, et al in [2] and suggest a related minimization problem for which we nd a lower bound. A graph G is an exact n-step domination graph if there is some set of vertices in G such that each vertex in the graph is distance n from exactly one vertex in the set. We prove that such subsets have order at least blog2 nc + 2 and limit how much better a bound is possible. We also prove a related conjecture of Alavi, et al [1] that if each vertex in a connected graph G has exactly one vertex distance n from it then the diameter is n unless G is a path consisting of 2n vertices.
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