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Representing Groups by Colourings of Graphs
Author(s) -
Baumann Ulrike
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19971880103
Subject(s) - mathematics , combinatorics , automorphism , isomorphism (crystallography) , graph , graph isomorphism , discrete mathematics , line graph , chemistry , crystal structure , crystallography
The topic of this paper is representing groups by edge‐coloured graphs. Every edge‐coloured graph determines a group of graph automorphisms which preserve the colours of the edges. An edge colouring of a graph G is called a perfect one iff every colour class is a perfect matching in G . We prove that every group H and all of its subgroups can be represented (up to isomorphism) by a group of colour preserving automorphisms related to some perfect colouring of the same graph.