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Some distance magic graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2018 A graph , where and is said to be a distance magic graph if there exists a bijection from the vertex set to the set such that, , for all , which is a constant and independent of , where is the open neighborhood of the vertex .
Aloysius Godinho, T. Singh
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Orientable -distance magic regular graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 Hefetz, Mütze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation (Hefetz et al., 2010). In this paper we support the analogous question for distance magic labeling. Let be an Abelian group of order .
Paweł Dyrlaga, Karolina Szopa
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The Distance Magic Index of a Graph [PDF]
Discussiones Mathematicae Graph Theory, 2018 Let G be a graph of order n and let S be a set of positive integers with |S| = n. Then G is said to be S-magic if there exists a bijection ϕ : V (G) → S satisfying ∑x∈N(u)ϕ(x) = k (a constant) for every u ∈ V (G). Let α(S) = max{s : s ∈ S}.
Godinho Aloysius +2 more
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Union of Distance Magic Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2017 A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ from V to the set {1, . . . , n} such that the weight w(x) = ∑y∈NG(x) ℓ(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant.
Cichacz Sylwia, Nikodem Mateusz
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Orientable ℤN-Distance Magic Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2019 Let G = (V, E) be a graph of order n. A distance magic labeling of G is a bijection ℓ: V → {1, 2, . . ., 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 open neighborhood of v.
Cichacz Sylwia +2 more
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Distance Magic Cartesian Products of Graphs [PDF]
Discussiones Mathematicae Graph Theory, 2016 A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant.
Cichacz Sylwia +3 more
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On 14-regular distance magic graphs [PDF]
Electronic Journal of Graph Theory and ApplicationsLet G be a graph with n vertices. By N(v) we denote the set of all vertices adjacent to v. A bijection f : V(G)→{1, 2, …, n} is a distance magic labeling of G if there exists an integer k such that the sum of labels of all vertices adjacent to v is k for
Petr Kovář, Matěj Krbeček
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Classification of tetravalent distance magic circulant graphs
Discrete Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Primoz Šparl, Stefko Miklavic
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A note on Distance Magic and Distance antimagic graphs
Electronic Notes in Discrete Mathematics, 2015 Abstract Let G = ( V , E ) be a graph of order n. The graph G is said to be distance magic if there exists a bijection f : V ( G ) → { 1 , 2 , … , n } such that for all v ∈ V , w ( v ) = ∑ u ∈ N ( v ) f ( u ) is a constant, called vertex magic constant.
Subramanian Arumugam
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Distance magic circulant graphs
Discrete Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sylwia Cichacz, Dalibor Fronček
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