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On Regular Distance Magic Graphs of Odd Order
Journal of Combinatorial Mathematics and Combinatorial Computing, 2023Let 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 +3 more
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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
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Distance Magic Labeling in Complete 4-partite Graphs [PDF]
Graphs and Combinatorics, 2015 Let $G$ be a complete $k$-partite simple undirected graph with parts of sizes $p_1\le p_2...\le p_k$. Let $P_j=\sum_{i=1}^jp_i$ for $j=1,...,k$. It is conjectured that $G$ has distance magic labeling if and only if $\sum_{i=1}^{P_j} (n-i+1)\ge j{{n+1}\choose{2}}/k$ for all $j=1,...,k$.
Daniel Kotlár
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Difference distance magic oriented graphs
Research in Mathematical SciencesAbstractThis article introduces difference distance magic (DDM) labelings, a new labeling on oriented graphs. We discuss basic properties of oriented graphs that have a DDM labeling and methods for constructing DDM labelings in a wide variety of oriented graph classes. We also give a variety of oriented graph classes that fail to produce a DDM labeling.
Alison Marr +2 more
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Distance magic labelings of graphs
Australas. J Comb., 2003Authors 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 +2 more
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Group distance magic labeling of tetravalent circulant graphs
Discrete Applied MathematicsLet \(G = (V , E)\) 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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Distance Magic and Distance Antimagic Labeling of Some Product Graphs
2020Distance 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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On distance magic labeling of graphs
2009Summary: Distance magic labeling of a graph of order \(n\) is a bijection \(f:V\to\{1,2,\dots,n\}\) with the property that there is a positive integer constant \(k\) such that for any vertex \(x\), \(\sum_{y\in N(x)}f(y)=k\), where \(N(x)\) is the set of vertices adjacent to \(x\).
Sugeng, K. A. +4 more
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Group distance magic set of group vertex magic graphs
Journal of Combinatorial Mathematics and Combinatorial Computing<p>Let <span class="math inline">\(G\)</span> be a graph of order <span class="math inline">\(n\)</span> and let <span class="math inline">\(A\)</span> be an additive Abelian group with identity 0. A mapping <span class="math inline">\(l : V(G) \to A \setminus \{0\}\)</span> is said to be a <span
S.V. Bharanedhar +3 more
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