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Matrices Associated with D-Distance Magic Graphs and Their Properties [PDF]

Cybernetics and Systems Analysis, 2019
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Semeniuta, M., Shulhin, V.
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Group distance magic labeling of tetravalent circulant graphs

Discrete Applied Mathematics
Let \(G = (V , E)\) be a finite simple graph of order \(n\) and let \(\Gamma\) be an abelian group of order \(n\). A \(\Gamma\)-distance magic labeling of \(G\) is a bijection \(\varphi :V\rightarrow \Gamma\) for which there exits \(\gamma \in \Gamma\) such that \(\Sigma_{x \in N(V)} \varphi(x)=\gamma\) for any \(v \in V\), where \(N(v)\) is the ...
Guixin Deng
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A Heuristic for Distance Magic Labeling [PDF]

Procedia Computer Science, 2015
A distance magic labeling of a graph G with magic constant k is a bijection λ from the V(G) into {1, 2,. . ., |V(G)|}, such that ∑u∈N(v) λ(u) = k for every vertex v.
Rinovia Simanjuntak
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Distance magic graphs G×Cn

Discrete Applied Mathematics, 2014
Sylwia Cichacz
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On Regular Distance Magic Graphs of Odd Order

Journal of Combinatorial Mathematics and Combinatorial Computing, 2023
Let G=(V,E) be a graph with n vertices. A bijection f:V→{1,2,…,n} is called a distance magic abeling f G if there exists an integer k such that ∑u∈N(v)f(u)=k for all v∈V, where N(v) is the set of all ertices adjacent to v. Any graph which admits a distance magic labeling is a distance magic graph.
Kovář, Petr, Silber, Adam, Kabelíková-Hrušková, Pavla, Kravčenko, Michal   +3 more
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On Nearly Distance Magic Graphs

2017
Let \(G=(V,E)\) be a graph on n vertices. A bijection \(f: V \rightarrow \{1,2,\ldots , n\}\) is called a nearly distance magic labeling of G if there exists a positive integer k such that \(\sum _{x \in N(v)} f(x)=k \ or \ k+1\) for every \(v \in V\). The constant k is called a magic constant of the graph and any graph which admits such a labeling is ...
Aloysius Godinho, Tarkeshwar Singh, S. Arumugam 0001   +2 more
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Distance magic labelings of graphs [PDF]

Australas. J Comb., 2003
Authors define 1-vertex-magic labelling of a graph \(G=(V,E)\) as a bijection \(f\colon \{1,2,\dots, |V|\} \to V\) such that for any two vertices \(u,v \in V\), \(\sum_{x\in N(u)}f(x)=\sum_{y\in N(v)}f(y)\). The authors solve the existence problem of 1-vertex-magic labellings on complete bipartite, tripartite and regular multipartite graphs.
Mirka Miller, Chris Rodger, Rinovia Simanjuntak   +2 more
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Distance magic labelings of Cartesian products of cycles [PDF]

Discrete Mathematics
A 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.
Šparl, Primož, Rozman, Ksenija
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Distance Magic and Distance Antimagic Labeling of Some Product Graphs

2020
Distance magic graph admits a distance magic labeling, whereas the distance antimagic graph admits a distance antimagic labeling. This chapter discusses the existence of distance magic labeling and distance antimagic labeling for a specific function. It considers that all graphs with a specific vertex set and a specific edge set are finite and simple ...
N P Shrimali, Y M Parmar
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