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Metric ends, fibers and automorphisms of graphs
Author(s) -
Krön Bernhard,
Möller Rögnvaldur G.
Publication year - 2008
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.200510587
Subject(s) - automorphism , mathematics , transitive relation , automorphisms of the symmetric and alternating groups , bounded function , invariant (physics) , metric space , graph , pure mathematics , combinatorics , automorphism group , action (physics) , discrete mathematics , mathematical analysis , mathematical physics , physics , quantum mechanics
Several results on the action of graph automorphisms on ends and fibers are generalized for the case of metric ends. This includes results on the action of the automorphisms on the end space, directions of automorphisms, double rays which are invariant under a power of an automorphism and metrically almost transitive automorphism groups. It is proved that the bounded automorphisms of a metrically almost transitive graph with more than one end are precisely the kernel of the action on the space of metric ends. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)