Perfect codes and regular partitions in graphs and groups
type: Item
instance of: scholarly article
title: Perfect codes and regular partitions in graphs and groups
zbMATH Open document ID: 0626.05051
DOI: 10.1016/S0195-6698(87)80004-5
author: Gwihen Etienne
published in: European Journal of Combinatorics
publication date: 1987-01-01T00:00:00Z
review text: The author's abstract states: ``We define the concept of regular partition of a graph \(\Gamma\) and its relationship to the automorphism group of \(\Gamma\). In application, we give necessary conditions for a perfect code of \(\Gamma\) in the sense of Biggs to exist. We recover a theorem of C. Landauer relating perfect codes in a finite group to its characters. We establish a necessary condition on the subgroups for the existence of a perfect code. As an application, we mention a result of O. Rothaus and J. G. Thompson concerning the existence of perfect codes in permutation groups.''
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 4016956
zbMATH Keywords: regular partition of a graph
zbMATH Keywords: automorphism group
zbMATH Keywords: perfect code
MaRDI profile type: Publication
cites work: Q4770409
cites work: On Permutation Cliques
cites work: Q3952285
cites work: Q5775434
cites work: A combinatorial problem in the symmetric group
description: scientific article; zbMATH DE number 4016956