On digraphs with circulant adjacent matrices
type: Item
instance of: scholarly article
title: On digraphs with circulant adjacent matrices
zbMATH Open document ID: 0677.05040
DOI: 10.1007/BF01190673
author: Chong-Yun Chao
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Let \(F_ n\) be the family of digraphs with n vertices consisting of n- cycles with circulant adjacency matrices. (1) We characterize the isomorphic digraphs in \(F_ n.\) (2) Let \(n=p_ 1^{k_ 1}p_ 2^{k_ 2}...p_ t^{k_ t}\) be the prime-power decomposition of the positive integer n. We show that the vector space, \(A(F_ n)\), of adjacency matrices of \(F_ n\) over the integers modulo 2 is \[ A(F_{p_ 1^{k_ 1}})\otimes A(F_{p_ 2^{k_ 2}})\otimes...\otimes A(F_{p_ t^{k_ t}}). \] (3) We use Pólya's theorem to enumerate \(F_ n\). We also use an algorithm to determine the digraphs in each of the equivalence classes in \(F_ n.\) (4) We present an algorithm to obtain the group of automorphisms for each digraph in \(F_ n\).
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 4108802
zbMATH Keywords: digraphs
zbMATH Keywords: circulant adjacency matrices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4108802