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If G is an exact n-step domination graph of diameter n and H is an exact m-step domination graph of diameter m, then the Cartesian product G×H is an exact (n+m)-step domination graph of diameter n+m with (n+m)-step dominating set S G ×S offisnail.info by: 3.

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A graph G with Vertex set V (G) is an exact n-step domination graph if there is some subset S C V(G) such that each vertex in G is distance n from exactly one vertex in S.

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n there is an exact-step domination graph G with j S G = n + 2 i where is the largest p o w er of whic h divides. Pr oof. Note that C 2(n +2 i) is an exact n-step domination graph. 2 W e conjecture the follo wing restriction on p ossible lo w er b ounds for order of exact n-step dominating sets. Conjecture 6. F or eac h n 5, there exists an.


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 find 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. Scott Nudelman, The modular n-queens problem in higher dimensions, Discrete Mathematics, () Jeffrey Vanderkam, Path-sequential labelling of cycles, Discrete Mathematics, () Patricia Hersh, Exact n-step domination graphs, Discrete Mathematics, () - Funded by NSF/NSA/UMD.
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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 blog 2 nc + 2 and limit how much better a bound is possible.

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Exact algorithms for weak Roman domination. We now describe our exact algorithms solving the Weak Roman Domination problem. Observe that this problem can trivially be solved in O ∗ (3 n) time by enumerating all three-partitions of the set of vertices, which Author: Mathieu Chapelle, Manfred Cochefert, Jean-Fraņcois Couturier, Dieter Kratsch, Romain Letourneur, Mat. On exact n-step domination, Ars Combinatoria, Volume LVIII, January, This was written when I attended the Duluth REU. Enumerating up-side self-avoiding walks, Electronic Journal of Combinatorics, Volume 3 (1), This was written when I was a high school student at RSI. Collaborators.

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