A Heuristic for Distance Magic Labeling
نویسندگان
چکیده
منابع مشابه
A \varGamma -magic Rectangle Set and Group Distance Magic Labeling
A Γ -magic rectangle set MRSΓ (a, b; c) of order abc is a collection of c arrays (a× b) whose entries are elements of group Γ , each appearing once, with all row sums in every rectangle equal to a constant ω ∈ Γ and all column sums in every rectangle equal to a constant δ ∈ Γ . In the paper we show that if a and b are both even then MRSΓ (a, b; c) exists for any Abelian group Γ of order abc. Fu...
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Let G = (V,E) be a graph of order n. A distance magic labeling of G is a bijection l : V → {1, . . . , n} for which there exists a positive integer k such that ∑ x∈N(v) l(x) = k for all v ∈ V , where N(v) is the neighborhood of v. We introduce a natural subclass of distance magic graphs. For this class we show that it is closed for the direct product with regular graphs and closed as a second f...
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Let G = (V,E) be a graph and Γ an abelian group, both of order n. A group distance magic labeling of G is a bijection : V → Γ for which there exists μ ∈ Γ such that ∑x∈N(v) (x) = μ for all v ∈ V, where N(v) is the neighborhood of v. Froncek [Australas. J. Combin. 55 (2013), 167–174] showed that the cartesian product Cm Cn, m,n ≥ 3 is a Zmn-distance magic graph if and only if mn is even. In this...
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A group distance magic labeling of a graph G(V, E) with |V | = n is an injection from V to an abelian group Γ of order n such that the sum of labels of all neighbors of every vertex x ∈ V is equal to the same element μ ∈ Γ. We completely characterize all Cartesian products Ck Cm that admit a group distance magic labeling by Zkm.
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A graph G is said to have a totally magic cordial labeling with constant C if there exists a mapping f : V (G) ∪ E(G) → {0, 1} such that f(a) + f(b) + f(ab) ≡ C (mod 2) for all ab ∈ E(G) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. In this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...
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ژورنال
عنوان ژورنال: Procedia Computer Science
سال: 2015
ISSN: 1877-0509
DOI: 10.1016/j.procs.2015.12.083