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On distance magic circulants of valency 6 [PDF]
, 2022 A graph $Γ= (V,E)$ of order $n$ is {\em distance magic} if it admits a bijective labeling $\ell \colon V \to \{1,2, \ldots, n\}$ of its vertices for which there exists a positive integer $κ$ such that $\sum_{u \in N(v)} \ell(u) = κ$ for all vertices $v ...
Miklavič, Štefko +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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Total Neighborhood Magic Labeling: A New Variant of Magic Labeling
, 2021 In this paper, we introduce a total neighborhood magic labeling, which is a variant of magic labeling.
N P Shrimali, Y M Parmar
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Single-Cell Dissection of Microglial Dysfunction in Diabetes-Associated Neurodegenerative Vulnerability. [PDF]
Adv Sci (Weinh)Using single‐cell transcriptomic and epigenomic profiling, researchers mapped microglial dysfunction across the lifespan of db/db mice. The authors uncovered a nonlinear microglial remodeling featuring early inflammatory priming, a mid‐stage transcriptional inflection, and late dysfunction.
Zhang J +6 more
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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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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 $j=1,...,k$.
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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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Distance antimagic labeling of join and corona of two graphs
AKCE International Journal of Graphs and Combinatorics, 2017 Let be a graph of order . Let be a bijection. The weight of a vertex with respect to is defined by , where is the open neighborhood of . The labeling is said to be distance antimagic if for every pair of distinct vertices .
A.K. Handa +3 more
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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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Distance Magic Labeling of Generalised Mycielskian Graphs
, 2023 In this paper, we have studied the distance magic labelling of Generalised Mycielskian of a few families of graphs.
Pawar, Ravindra, Singh, Tarkehswar
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