Results 11 to 20 of about 29,683 (234)
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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A note on incomplete regular tournaments with handicap two of order n≡8(mod 16) [PDF]
Opuscula Mathematica, 2017 A \(d\)-handicap distance antimagic labeling of a graph \(G=(V,E)\) with \(n\) vertices is a bijection \(f:V\to \{1,2,\ldots ,n\}\) with the property that \(f(x_i)=i\) and the sequence of weights \(w(x_1),w(x_2),\ldots,w(x_n)\) (where \(w(x_i)=\sum_{x_i
Dalibor Froncek
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Note on group distance magic graphs $G[C_4]$ [PDF]
, 2012 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 $x \in V$
D. Froncek +3 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 Kovár
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Regular graphs of odd degree are antimagic [PDF]
, 2013 An antimagic labeling of a graph $G$ with $m$ edges is a bijection from $E(G)$ to $\{1,2,\ldots,m\}$ such that for all vertices $u$ and $v$, the sum of labels on edges incident to $u$ differs from that for edges incident to $v$.
Cranston, Daniel W.
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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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Handicap Labelings of 4-Regular Graphs
Advances in Electrical and Electronic Engineering, 2017 Let G be a simple graph, let f : V(G)→{1,2,...,|V(G)|} be a bijective mapping. The weight of v ∈ V(G) is the sum of labels of all vertices adjacent to v. We say that f is a distance magic labeling of G if the weight of every vertex is the same
Petr Kovar +3 more
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Distance antimagic labelings of Cartesian product of graphs
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a graph of order n. Let be a bijection. The weight w(v) of a vertex v with respect to the labeling f is defined by where N(v) is the open neighborhood of v. The labeling f is called a distance antimagic labeling if for any two distinct vertices v1,
Nancy Jaseintha Cutinho +2 more
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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 +2 more
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Orientable Group Distance Magic Labeling of Directed Graphs
Mathematical Problems in Engineering, 2022 A directed graph G is said to have the orientable group distance magic labeling if there exists an abelian group ℋ and one-one map ...
Wasim Ashraf +2 more
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