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$k$-Distance Magic Labeling and Long Brush Graphs [PDF]

, 2022
We define a labeling $f:$ $V(G)$ $\rightarrow$ $\{1, 2, \ldots, n\}$ on a graph $G$ of order $n \geq 3$ as a \emph{$k$-distance magic} ($k$-DM) if $\sum_{w\in \partial N_k(u)}{ f(w)}$ is a constant and independent of $u\in V(G)$ where $\partial N_k(u)$ = $\{v\in V(G): d(u, v) = k\}$, $k\in\mathbb{N}$. Graph $G$ is called a \emph{$k$-DM} if it has a $k$-
V. Vilfred Kamalappan
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Examples of distance magic labelings of the $6$-dimensional hypercube [PDF]

, 2021
A distance magic labeling of an $n$-dimensional hypercube is a labeling of its vertices by natural numbers from $\{0, \ldots, 2^n-1\}$, such that for all vertices $v$ the sum of the labels of the neighbors of $v$ is the same. Such a labeling is called neighbor-balanced, if, moreover, for each vertex $v$ and an index $i=0,\ldots,n-1$, exactly half of ...
Petr Savický
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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, Singh Tarkeshwar, Arumugam S.   +2 more
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A magic-angle-spinning NMR method for H1–H1 distance measurement using coherent polarization transfer in C13-labeled organic solids [PDF]

The Journal of Chemical Physics, 2008
We have developed a theory for H1–H1 distance measurements from the direct polarization transfer in C13-labeled solids under magic-angle spinning. The polarization transfer caused by the H1–H1 dipolar interactions was analyzed with zeroth-order average Hamiltonian for a H1–C13–C13–H1 spin system in the frame modulated by C13–H1 dipolar interactions and
Hiroki Takahashi, Hideo Akutsu, Toshimichi Fujiwara   +2 more
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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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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, Freyberg Bryan, Froncek Dalibor   +2 more
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Distance magic labelings of hypercubes

Electronic Notes in Discrete Mathematics, 2013
Abstract A distance magic labeling of a graph G is a bijective assignment of labels from {1, 2, …, |V (G)|} to the vertices of G such that the sum of labels on neighbors of u is the same for all vertices u. We show that the n-dimensional hypercube has a distance magic labeling for every n ≡ 2 ( mod 4 ) . It is known that this condition is
Petr Gregor, Petr Kovář
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Distance magic labelings of Cartesian products of cycles

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. In this paper we classify all distance magic Cartesian products of two cycles, thereby correcting an error in a widely cited paper from 2004.
Ksenija Rozman, Primož Šparl
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On D-distance (anti)magic labelings of shadow graph of some graphs [PDF]

Electronic Journal of Graph Theory and Applications
Summary: Let \(G\) be a graph with vertex set \(V(G)\) and diameter \(\operatorname{diam}(G)\). Let \(D\subseteq \{0, 1, 2, 3, \dots, \operatorname{diam}(G)\}\) and \(\varphi : V(G) \rightarrow \{1, 2, 3, \dots, |V(G)|\}\) be a bijection. The graph \(G\) is called \(D\)-\textit{distance magic}, if \(\sum_{s \in N_D(t)} \varphi (s)\) is a constant for ...
Anak Agung Gede Ngurah, Nur Inayah, M. I. S. Musti   +2 more
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Corrigendum to: On zero sum-partition of Abelian groups into three sets and group distance magic labeling

Ars Mathematica Contemporanea, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sylwia Cichacz
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