On \(k\)-complementing permutations of cyclically \(k\)-complementary graphs
type: Item
instance of: scholarly article
title: On \(k\)-complementing permutations of cyclically \(k\)-complementary graphs
zbMATH Open document ID: 0858.05088
DOI: 10.1016/0012-365X(94)00082-T
author: Jose M. Bernaldez
published in: Discrete Mathematics
publication date: 1997-03-11T00:00:00Z
review text: Let \(K_n\) be a complete graph and \(H_1,H_2,\dots,H_k\) its isomorphic factorization where \(k>1\) and \(k\) divides \({1\over 2n} (n-1)\). Let \(\beta\) be a permutation on \(V(K_n)\) such that (by a suitable rearrangement of \(H_i\)) \(\beta: V(H_i)\to V(H_{i+1})\) is an isomorphism for \(i=1,2,\dots,k-1\). Then any isomorphical image of a factor \(H_i\) is said to be a cyclically \(k\)-complementary graph \(G(k,n)\). The permutation \(\beta\) is called a \(k\)-complementing permutation of \(G(k,n)\). The author gives necessary and sufficient conditions to be a power \(\beta^t\) of a \(k\)-complementing permutation \(\beta\) of \(G(k,n)\): (1) an automorphism of \(G(k,n)\), and (2) a \(k\)-complementing permutation of \(G(k,n)\). Further, he gives some special results which follow from a decomposition \(\beta= \beta_1\beta_2\cdots\beta_r\) of a \(k\)-complementing permutation \(\beta\) of \(G(k,n)\).
reviewed by: M.Koman
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 896527
zbMATH Keywords: factorization
zbMATH Keywords: permutation
zbMATH Keywords: isomorphism
zbMATH Keywords: \(k\)-complementary graph
zbMATH Keywords: \(k\)-complementing permutation
MaRDI profile type: Publication
cites work: On cyclically \(K\)-complementary graphs
cites work: The divisibility theorem for isomorphic factorizations of complete graphs
full work available at URL: 0012-365x(94)00082-t
OpenAlex ID: W2000954682
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description: scientific article; zbMATH DE number 896527