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Matrices Associated with D-Distance Magic Graphs and Their Properties
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Semeniuta, M., Shulhin, V.
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Distance magic circulant graphs
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Sylwia Cichacz, Dalibor Fronček
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Classification of tetravalent distance magic circulant graphs
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Primoz Šparl, Stefko Miklavic
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A note on Distance Magic and Distance antimagic graphs
Abstract Let G = ( V , E ) be a graph of order n. The graph G is said to be distance magic if there exists a bijection f : V ( G ) → { 1 , 2 , … , n } such that for all v ∈ V , w ( v ) = ∑ u ∈ N ( v ) f ( u ) is a constant, called vertex magic constant.
Subramanian Arumugam, A Ramalakshmi
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Spectra of graphs and closed distance magic labelings
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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Distance Magic Labeling and Two Products of Graphs [PDF]
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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On Nearly Distance Magic Graphs
Lecture Notes in Computer Science, 2017Let \(G=(V,E)\) 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
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Group distance magic and antimagic graphs [PDF]
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Sanming Zhou +2 more
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In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,…,|V(G)|} in such a way that the sum of all the vertex labels that are a ...
Alison Marr, Rinovia Simanjuntak
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