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Orientable Group Distance Magic Labeling of Directed Graphs [PDF]
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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Distance magic labelling of Mycielskian graphs [PDF]
Electronic Journal of Graph Theory and ApplicationsSummary: A 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 \(f : V(G) \rightarrow \{1, 2, \dots, n\}\) such that the vertex weight \(w(u)= \sum_{v\in N(u)}f(v)=k\) is constant and independent of \(u\), where \(N(u)\) is an open neighborhood of the vertex \(u\). The constant \(k\)
Ravindra Kuber Pawar, T. C. N. SINGH
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On distance magic labelings of Hamming graphs and folded hypercubes
Discussiones Mathematicae Graph Theory, 2021 Summary: 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, Primož Šparl
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Self-reverse labelings of distance magic graphs [PDF]
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. We introduce the concept of a self-reverse distance magic labeling of a regular graph which allows for a more compact ...
Petr Kovář +2 more
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On D-distance (anti)magic labelings of shadow graph of some graphs [PDF]
Electronic Journal of Graph Theory and ApplicationsSummary: Let \(G\) be a graph with vertex set \(V(G)\) and diameter \(\operatorname{diam}(G)\). Let \(D\subseteq \{0, 1, 2, 3, \dots, \operatorname{diam}(G)\}\) and \(\varphi : V(G) \rightarrow \{1, 2, 3, \dots, |V(G)|\}\) be a bijection. The graph \(G\) is called \(D\)-\textit{distance magic}, if \(\sum_{s \in N_D(t)} \varphi (s)\) is a constant for ...
Anak Agung Gede Ngurah +2 more
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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 ...
Ehab Ebrahem +2 more
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On zero sum-partition of Abelian groups into three sets and group distance magic labeling
Ars Mathematica Contemporanea, 2017 Summary: We say that a finite abelian group \(\Gamma\) has the constant-sum-partition property into \(t\) sets (CSP\((t)\)-property) if for every partition \(n=r_1+r_2+\dots +r_t\) of \(n\), with \(r_i\geq 2\) for \(2\leq i\leq t\), there is a partition of \(\Gamma\) into pairwise disjoint subsets \(A_1,A_2,\dots ,A_t\), such that \(A_i=r_i\) and for ...
Sylwia Cichacz
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Ars Mathematica Contemporanea, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sylwia Cichacz
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Distance Magic Labeling of Corona Product of Graphs
InPrime: Indonesian Journal of Pure and Applied MathematicsLet 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. If the labeling f satisfies that there exists a constant k such that w(v)=k, for every vertex v in the graph G, then f is called a ...
Christyan Tamaro Nadeak
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Group distance magic labeling of direct product of graphs
Ars Mathematica Contemporanea, 2014 A distance magic labeling of a graph of order \(n\) is a bijection from the vertex set to \(\{0,1,\dots,n-1\}\) such that the sum of neighbors of any vertex is the same. Magic labellings of graphs have been studied as a generalization of magic squares. A central question has been to identify which graphs admit such labelings.
Marcin Anholcer +3 more
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