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Symmetry Groups of Coloured Graphs
Author(s) -
Baumann Ulrike
Publication year - 1993
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.19931630109
Subject(s) - mathematics , combinatorics , automorphism , graph automorphism , vertex (graph theory) , coset , graph isomorphism , graph , isomorphism (crystallography) , symmetric graph , discrete mathematics , voltage graph , line graph , chemistry , crystal structure , crystallography
A perfect colouring Φ of a simple undirected connected graph G is an edge colouring such that each vertex is incident with exactly one edge of each colour. This paper concerns the problem of representing groups by graphs with perfect colourings. We define groups of graph automorphisms, which preserve the structure of the colouring, and characterize these groups up to isomorphism. Our considerations are based on the fact that every perfectly coloured graph is isomorphic to a Schreier coset graph on a group generated by involutions.