Results 11 to 20 of about 2,348 (174)
DISTANCE MAGIC GRAPHS - A SURVEY [PDF]
Journal of the Indonesian Mathematical Society, 2012 Let <i>G = (V;E)</i> be a graph of order n. A bijection <i>f : V → {1, 2,...,n} </i>is called <i>a distance magic labeling </i>of G if there exists a positive integer k such that <i>Σ f(u) = k </i> for all <i>v ε V</i>, where <i>N(v)</i> is the open ...
S. Arumugam +2 more
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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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Note on group distance magicness on product graphs [PDF]
Contributions to Discrete Mathematics, 2021 If $l$ is a bijection from the vertex set $V(G)$ of a graph $G$ to an additive abelian group $\Gamma$ of $|V(G)|$ elements such that for any vertex $u$ of $G$, the weight $\sum_{v\in N_{G}(u)}l(v)$ is $\mu$, where $\mu \in \Gamma$, then $l$ is a $\Gamma$-distance magic labeling of $G$.
Prajeesh, Appattu Vallapil +1 more
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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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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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D-magic strongly regular graphs
AKCE International Journal of Graphs and Combinatorics, 2020 For a set of distances D, a graph G on n vertices is said to be D-magic if there exists a bijection and a constant k such that for any vertex x, where is the D-neighbourhood set of x.
Rinovia Simanjuntak, Palton Anuwiksa
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Spectra of graphs and closed distance magic labelings
Discrete Mathematics, 2016 Let $G=(V,E)$ be a graph of order $n$. A closed distance magic labeling of $G$ is a bijection $\ell \colon V(G)\rightarrow \{1,\ldots ,n\}$ 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 closed neighborhood of $v$.
Marcin Anholcer +2 more
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On the uniqueness of d-vertex magic constant [PDF]
Discussiones Mathematicae Graph Theory, 2014 Let G = (V,E) be a graph of order n and let D ⊆ {0, 1, 2, 3, . . .}. For v ∈ V, let ND(v) = {u ∈ V : d(u, v) ∈ D}. The graph G is said to be D-vertex magic if there exists a bijection f : V (G) → {1, 2, . . .
Arumugam S. +2 more
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On Distance Magic Harary Graphs [PDF]
, 2018 This paper establishes two techniques to construct larger distance magic and (a, d)-distance antimagic graphs using Harary graphs and provides a solution to the existence of distance magicness of legicographic product and direct product of G with C4, for every non-regular distance magic graph G with maximum degree |V(G)|-1.
Prajeesh, A V, Paramasivam, Krishnan
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Note on Group Distance Magic Graphs G[C 4] [PDF]
Graphs and Combinatorics, 2013 A \emph{group distance magic labeling} or a $\gr$-distance magic labeling of a graph $G(V,E)$ with $|V | = n$ is an injection $f$ from $V$ to an Abelian group $\gr$ of order $n$ such that the weight $w(x)=\sum_{y\in N_G(x)}f(y)$ of every vertex $x \in V$ is equal to the same element $μ\in \gr$, called the magic constant. In this paper we will show that
Sylwia Cichacz, Cichacz Sylwia
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