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A SURVEY OF DISTANCE MAGIC GRAPHS [PDF]
, 2020 In this report, we survey results on distance magic graphs and some closely related graphs. A distance magic labeling of a graph G with magic constant k is a bijection l from the vertex set to {1, 2, . . .
Rupnow, Rachel
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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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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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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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On distance magic labelings of Hamming graphs and folded hypercubes [PDF]
Discussiones Mathematicae Graph TheorySummary: Let \(\Gamma =(V,E)\) be a graph of order \(n\). A distance magic labeling of \(\Gamma\) is a bijection \(\ell \colon V \to \{1,2, \ldots, n\}\) for which there exists a positive integer \(k\) such that \(\sum_{x \in N(u)} \ell(x) = k\) for all vertices \(u \in V\), where \(N(u)\) is the neighborhood of \(u\).
Štefko Miklavič, Primoz Šparl
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On 14-regular distance magic graphs
Electronic Journal of Graph Theory and ApplicationsLet G be a graph with n vertices. By N(v) we denote the set of all vertices adjacent to v. A bijection f : V(G)→{1, 2, …, n} is a distance magic labeling of G if there exists an integer k such that the sum of labels of all vertices adjacent to v is k for
Petr Kovář, Matěj Krbeček
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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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Constant Sum Partition of Sets of Integers and Distance Magic Graphs
Discussiones Mathematicae Graph Theory, 2018 Let A = {1, 2, . . . , tm+tn}. We shall say that A has the (m, n, t)-balanced constant-sum-partition property ((m, n, t)-BCSP-property) if there exists a partition of A into 2t pairwise disjoint subsets A1, A2, . . . , At, B1, B2, . . .
Cichacz Sylwia, Gőrlich Agnieszka
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Self-Reverse Labelings of Distance Magic Graphs
Bulletin of the Malaysian Mathematical Sciences SocietyAbstract A graph is distance magic if it admits a bijective labeling of its vertices by integers from 1 up to the order of the graph in such a way that the sum of the labels of all the neighbors of a vertex is independent of a given vertex.
Petr Kovář +2 more
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On D-distance (anti)magic labelings of shadow graph of some graphs
Electronic Journal of Graph Theory and ApplicationsLet G be a graph with vertex set V(G) and diameter diam(G). Let D ⊆ {0, 1, 2, 3, …, diam(G)} and φ : V(G)→{1, 2, 3, …, |V(G)|} be a bijection. The graph G is called D-distance magic, if s ∈ ND(t)φ(s) is a constant for any vertex t ∈ V(G). The graph G is
Anak Agung Gede Ngurah +2 more
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