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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
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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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Union of Distance Magic Graphs
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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The Distance Magic Index of a Graph
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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Distance Magic Cartesian Products of Graphs
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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Orientable ℤN-Distance Magic Graphs
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 Labeling and Two Products of Graphs [PDF]
Graphs and Combinatorics, 2014 Let $G=(V,E)$ be a graph of order $n$. A distance magic labeling of $G$ is a bijection $\ell \colon V\rightarrow {1,...,n}$ for which there exists a positive integer $k$ such that $\sum_{x\in N(v)}\ell (x)=k$ for all $v\in V $, where $N(v)$ is the neighborhood of $v$. We introduce a natural subclass of distance magic graphs. For this class we show that
Marcin Anholcer +2 more
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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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On constant sum partitions and applications to distance magic-type graphs
AKCE International Journal of Graphs and Combinatorics, 2020 Let be an additive abelian group of order and let be a partition of where A constant sum partition (or -sum partition) of is a pairwise disjoint union of subsets such that and for some fixed and every In 2009, Kaplan, Lev, and Roditty proved that a 0-sum
Bryan Freyberg
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Group distance magic and antimagic graphs [PDF]
Electronic Notes in Discrete Mathematics, 2015 Final ...
Sylwia Cichacz +2 more
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