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Automorphism groups of graphs with 1-factorizations

✍ Scribed by Ulrike Baumann

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 523 KB
Volume: 158
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00065-5

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✦ Synopsis

A l-factorization cp of a simple undirected connected graph G is an edge colouring such that each vertex is incident with exactly one edge of each colour. The automorphisms which preserve the colours of all edges constitute a group A,(G, q). We prove every finitely generated group H to be isomorphic to the full group A,(G,cp) for a regular graph G of degree 3 with a l-factorization cp. Moreover we show that for every finitely generated group H there is a regular graph G of degree 5 such that the group H and all of its subgroups can be represented (up to isomorphism) by a group of colour preserving automorphisms related to some l-factorization cp of G.

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