Circulant double coverings of a circulant graph of valency five
type: Item
instance of: scholarly article
title: Circulant double coverings of a circulant graph of valency five
zbMATH Open document ID: 1110.05081
publication date: 2006-12-13T00:00:00Z
review text: In the present paper, the authors carry on the study of isomorphism classes of circulant double coverings of circulant graphs (where a covering is called circulant if its covering graph is circulant). In [Discrete Math. 277, 73--85 (2004; Zbl 1033.05081)], they already enumerated the isomorphism classes of circulant double coverings of a certain kind, called typical, and showed as a consequence that no double covering of a circulant graph of valency three is circulant. Further, in [Graphs Comb. 21, 385-400 (2005; Zbl 1090.05056)], the isomorphism classes of connected circulant double coverings of a circulant graph of valency four were enumerated. Now, they obtain the following result on the number of isomorphism classes of circulant double coverings of a circulant graph of valency five: Let \(n\) be even and \(G=\text{Cay}(\mathbb Z_n, \{\pm i,\pm j, \frac n 2\})\) be a connected circulant graph of valency 5 with order \(n,\) where \(0 < i \neq j \leq \frac n 2.\) Then the number of isomorphism classes of circulant double coverings of \(G\) is 1 if \(i + j = \frac n 2,\) and 0 otherwise.
reviewed by: Maria Rita Casali
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 5079994
zbMATH Keywords: graph covering
zbMATH Keywords: voltage assignment
zbMATH Keywords: Cayley graph
zbMATH Keywords: isomorphism classes
author: Rongquan Feng
author: Jin Ho Kwak
MaRDI profile type: Publication
full work available at URL: s10114-005-0773-4
OpenAlex ID: W2041400354
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cites work: Enumeration of connected graph coverings
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cites work: Circulant double coverings of a circulant graph of valency four
DOI: 10.1007/S10114-005-0773-4
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5079994