\(D\)-magic labelings of the folded \(n\)-cube
type: Item
instance of: scholarly article
title: \(D\)-magic labelings of the folded \(n\)-cube
zbMATH Open document ID: 1469.05152
author: Yi Tian
author: Bo Hou
author: Li-hang Hou
author: Suogang Gao
published in: Discrete Mathematics
publication date: 2021-07-08T00:00:00Z
review text: Let $G$ be a finite undirected simple connected graph with vertex set $V(G)$, distance function $\delta$ and diameter $d$. Let $D\subset\{0,1,\dots,d\}$ be a set of distances. A bijection $l:V(G)\to\{0,1,\dots,|V(G)|\}$ is called a $D$-magic labeling of $G$ if there exists a constant $k$ such that $\sum_{x\in N_D(V)}l(x)=k$ for any vertex $v\in V(G)$, where $N_D(v)=\{x\in V(G):\delta(x,v)\in D\}$. $G$ has a $D$-magic labeling if $G$ admits a $D$-magic labeling. In this paper, the authors prove that the folded $n$-cube has a $\{1\}$-magic if and only if $n\equiv 0\pmod4$.
reviewed by: P. Jeyanthi
Mathematics Subject Classification ID: 05C78
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 7369648
zbMATH Keywords: \(D\)-magic labeling
zbMATH Keywords: distance-regular graph
zbMATH Keywords: folded \(n\)-cube
MaRDI profile type: Publication
full work available at URL: j.disc.2021.112520
OpenAlex ID: W3173427121
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DOI: 10.1016/J.DISC.2021.112520
description: scientific article; zbMATH DE number 7369648