Isomorphisms of circulant digraphs of degree 3
type: Item
instance of: scholarly article
title: Isomorphisms of circulant digraphs of degree 3
zbMATH Open document ID: 0856.05048
DOI: 10.1007/BF02662186
author: Zhihua Du
author: Qiongxiang Huang
published in: Applied Mathematics. Series B (English Edition)
publication date: 1996-09-24T00:00:00Z
review text: The circulant directed graph with \(n\) vertices and with characteristic set \(S = \{s_1, s_2, \dots, s_k\}\) is denoted by \(C_n (S)\). An isomorphism \(f\) from \(C_n (S)\) to \(C_n (T)\) (where \(|S |= |T |)\) is called zero-preserving if \(f(0) = 0\); among these, \(f\) is said to be special if \((\forall i)\) \([f(i) \equiv \lambda i \pmod n]\) for a \(\lambda\) which is relatively prime to \(n\). In Theorem 1 the graph pairs \((C_n (S), C_n (T))\) are characterized for which any zero-preserving isomorphism from \(C_n (S)\) to \(C_n (T)\) is a special isomorphism. The main results of the paper (Theorems 2 and 3) concern the particular case \(k (= |S |) = 3\). They are stated after a sequence of lemmas. The (three-element) sets \(S\) for which there exists a zero-preserving non-special isomorphism from \(C_n (S)\) are completely determined. Some consequences of Theorem 1 for the automorphisms of \(C_n (S)\) are also derived.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C60
zbMATH DE Number: 913300
zbMATH Keywords: circulant digraphs
zbMATH Keywords: graph pairs
zbMATH Keywords: isomorphism
zbMATH Keywords: automorphisms
reviewed by: A. Ádám
MaRDI profile type: Publication
cites work: Isomorphism of circulant graphs and digraphs
cites work: Circulants and their connectivities
cites work: Graphs with circulant adjacency matrices
cites work: Q3469128
cites work: A note on Adam's conjecture
cites work: A survey: Hamiltonian cycles in Cayley graphs
full work available at URL: https://doi.org/10.1007/bf02662186
OpenAlex ID: W2017193015
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description: scientific article; zbMATH DE number 913300