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Distance magic labelings of Cartesian products of cycles
Discrete MathematicsA graph of order $n$ is distance magic if it admits a bijective labeling of its vertices with integers from $1$ to $n$ such that each vertex has the same sum of the labels of its neighbors. In this paper we classify all distance magic Cartesian products of two cycles, thereby correcting an error in a widely cited paper from 2004.
Primoz Sparl
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An Infinite Family of Counterexamples to a Conjecture on Distance Magic Labeling
Experimental MathematicsThis work is about a partition problem which is an instance of the distance magic graph labeling problem. Given positive integers $n,k$ and $p_1\le p_2\le \cdots\le p_k$ such that $p_1+\cdots+p_k=n$ and $k$ divides $\sum_{i=1}^ni$, we study the problem of characterizing the cases where it is possible to find a partition of the set $\{1,2,\ldots,n ...
Ehab Ebrahem, Shlomo Hoory, Dani Kotlar
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Note on the Group Distance Magic Labeling of Direct Product of Two Cycles
Bulletin of the Iranian Mathematical SocietyzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guixin Deng
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Fuzzy magic labeling of simple graphs
Journal of Applied Mathematics and Computing, 2018R A Borzooei, Mohammad Hamidi
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Orientable Z_n-distance magic labeling of the Cartesian product of many cycles [PDF]
Electronic Journal of Graph Theory and Applications, 2017 The following generalization of distance magic graphs was introduced in [2]. A directed Z_n-distance magic labeling of an oriented graph $\overrightarrow{G}=(V,A)$ of order n is a bijection $\overrightarrow{\ell}\colon V \rightarrow Z_n$ with the ...
Bryan Freyberg, Melissa Keranen
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Distance magic labelling of Mycielskian graphs
Electronic Journal of Graph Theory and ApplicationsA graph G = (V, E), where |V(G)| = n and |E(G)| = m is said to be a distance magic graph if there is a bijection f : V(G)→{1, 2, …, n} such that the vertex weight w(u)=∑v ∈ N(u)f(v)=k is constant and independent of u, where N(u) is an open neighborhood ...
Ravindra Kuber Pawar, Tarkeshwar Singh
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AKCE International Journal of Graphs and Combinatorics, 2018 A graph G = ( V , E ) , where | V | = n and | E | = m is said to be a distance magic graph if there exists a bijection from the vertex set V to the set { 1 , 2 , … , n } such that, ∑ v ∈ N ( u ) f ( v ) = k , for all u ∈ V , which is a constant and ...
Aloysius Godinho, T. Singh
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On D-distance (anti)magic labelings of shadow graph of some graphs
Electronic Journal of Graph Theory and ApplicationsLet G be a graph with vertex set V(G) and diameter diam(G). Let D ⊆ {0, 1, 2, 3, …, diam(G)} and φ : V(G)→{1, 2, 3, …, |V(G)|} be a bijection. The graph G is called D-distance magic, if s ∈ ND(t)φ(s) is a constant for any vertex t ∈ V(G). The graph G is
Anak Agung Gede Ngurah +2 more
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On distance labelings of 2-regular graphs
Electronic Journal of Graph Theory and Applications, 2021 Let G be a graph with |V(G)| vertices and ψ : V(G) → {1, 2, 3, ... , |V(G)|} be a bijective function. The weight of a vertex v ∈ V(G) under ψ is wψ(v) = ∑u ∈ N(v)ψ(u). The function ψ is called a distance magic labeling of G, if wψ(v) is a constant for
Anak Agung Gede Ngurah +1 more
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Orientable -distance magic regular graphs
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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