Group Distance Magic Labeling of \(C_n^r\)

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• 关键词：Group distance magic labeling ; Circulant graphs
• 刊名：Lecture Notes in Computer Science
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：10156
• 期：1
• 页码：187-192
• 丛书名：Algorithms and Discrete Applied Mathematics
• ISBN：978-3-319-53007-9
• 卷排序：10156

文摘

Let \(G=(V,E)\) be a graph and \(\varGamma \) be an abelian group both of order n. For \(D \subset \{0,1,\ldots , diam(G)\}\), the D-distance neighbourhood of a vertex v in G is defined to be the set \(N_D(v)=\{x \in V \ | \ d(x,v) \in D\}\). A bijection \(f: V \rightarrow \varGamma \) is called a \((\varGamma , D)\)-distance magic labeling of G if there exists an \(\alpha \in \varGamma \) such that \(\sum _{x \in N_D(v)} f(x)=\alpha \) for every \(v \in V\). In this paper we study \((\varGamma , D)\)-distance magic labeling of the graph \(C_n^r\) for \(D=\{d\}\). We obtain \((\varGamma , \{d\})\)-distance magic labelings of \(C_n^r\) with respect to certain classes of abelian groups. We also obtain necessary conditions for existence of such labelings.