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Orientable Z_n-distance magic labeling of the Cartesian product of many cycles [PDF]
Electronic Journal of Graph Theory and Applications, 2017 The following generalization of distance magic graphs was introduced in [2]. A directed Z_n-distance magic labeling of an oriented graph $\overrightarrow{G}=(V,A)$ of order n is a bijection $\overrightarrow{\ell}\colon V \rightarrow Z_n$ with the ...
Bryan Freyberg, Melissa Keranen
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A Heuristic for Distance Magic Labeling [PDF]
Procedia Computer Science, 2015 AbstractA distance magic labeling of a graph G with magic constant k is a bijection λ from the V(G) into {1, 2,. . ., |V(G)|}, such that ∑u∈N(v) λ(u) = k for every vertex v. Here we present a heuristic algorithm for finding distance magic graphs and utilise it to find all distance magic graphs with at most 9 vertices.
Rinovia Simanjuntak
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Some distance magic graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2018 A graph G = ( V , E ) , where | V | = n and | E | = m is said to be a distance magic graph if there exists a bijection from the vertex set V to the set { 1 , 2 , … , n } such that, ∑ v ∈ N ( u ) f ( v ) = k , for all u ∈ V , which is a constant and ...
Aloysius Godinho, T. Singh
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Distance Magic Labeling and Two Products of Graphs [PDF]
Graphs and Combinatorics, 2014 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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Distance magic labelings of Cartesian products of cycles [PDF]
Discrete MathematicsA 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, Primoz Sparl
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An Infinite Family of Counterexamples to a Conjecture on Distance Magic Labeling [PDF]
Experimental MathematicsThis work is about a partition problem which is an instance of the distance magic graph labeling problem. Given positive integers $n,k$ and $p_1\le p_2\le \cdots\le p_k$ such that $p_1+\cdots+p_k=n$ and $k$ divides $\sum_{i=1}^ni$, we study the problem of characterizing the cases where it is possible to find a partition of the set $\{1,2,\ldots,n ...
Shlomo Hoory
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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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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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Distance Magic Labeling of Corona Product of Graphs
InPrimeLet G = (V, E) is a graph with order n, and f: V(G) → {1,2,...,n} is a bijection. For any vertex v ϵ V, the sum of f(u) is called the weight of vertex v, denoted by w(v), where N(v) is the set of neighbors of vertex v.
Christyan Tamaro Nadeak
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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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