Labelings in Cayley digraphs
type: Item
instance of: scholarly article
title: Labelings in Cayley digraphs
zbMATH Open document ID: 1230.05257
author: K. Thirusangu
author: Atulya K. Nagar
author: R. Raja Rajeswari
published in: European Journal of Combinatorics
publication date: 2010-11-22T00:00:00Z
review text: Graph labeling, introduced by \textit{A. Rosa} in [``On certain valuations of the vertices of a graph,'' Theory Graphs, Int. Symp. Rome 1966, 349--355 (1967; Zbl 0193.53204)], deals with assigning integers to the vertices or edges or both satisfying some combinatorial constraint. Labeled graphs serve as useful models for numerous applications such as a circuit design, radar, communication network, etc. There are different kinds of labelings, but to study labeling of Cayley graphs a new kind of labeling called super-vertex \((a,d)\)-antimagic labeling for digraphs was introduced. In this paper, the authors show the existence of supervertex \((a,d)\)-antimagic labeling and vertex-magic total labeling for some Cayley digraphs. The following are the main theorems: Theorem 1: The Cayley digraph associated with dihedral group \(D_n\) admits super-vertex \((a,d)\)-antimagic labeling. Theorem 2: The Cayley digraph associated with the group \(Z_n\) with the generating set \((a,b,b+k)\) admits magic labeling. Illustrative examples to support both results above have been provided for \(n=8\), and \(12\). An algorithm for obtaining super-vertex \((a,d)\)-antimagic labeling for the Cayley digraphs associated with \(D_n\), and also an algorithm for getting magic labeling for the Cayley digraphs associated with the \(Z_n\) group.
reviewed by: D. V. Chopra
Mathematics Subject Classification ID: 05C78
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 5817924
MaRDI profile type: Publication
full work available at URL: j.ejc.2010.07.006
OpenAlex ID: W2027575312
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DOI: 10.1016/J.EJC.2010.07.006
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description: scientific article; zbMATH DE number 5817924