Abstract
LexX be anm-connected infinite graph without subgraphs homeomorphic toKm, n, for somen, and let α be an automorphism ofX with at least one cycle of infinite length. We characterize the structure of α and use this characterization to extend a known result about orientation-preserving automorphisms of finite plane graphs to infinite plane graphs. In the last section we investigate the action of α on the ends ofX and show that α fixes at most two ends (Theorem 3.2).
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References
L. Babai, Groups of Graphs on Given Surfaces,Acta Math. Acad. Scient. Hungaricae 24 (1973), 215–221.
L. Babai andW. Imrich, Sense Preserving Groups of Polyhedral Graphs,Monatsh. f. Math. 79 (1975), 1–2.
H. Fleischner, Die Struktur der Automorphismen spezieller, endlicher, ebener, dreifach-knotenzusammenhängender Graphen,Compositio Math. 23 (1971), 435–444.
R. Halin, Über unendliche Wege in Graphen,Math. Annalen 157 (1964), 125–137.
R. Halin, Automorphisms and Endomorphisms of Infinite Locally Finite Graphs,Abhandlungen a.d. mathematischen Seminar der Universität Hamburg (1973), 251–283.
W. Imrich, On Automorphisms of Graphs with Forbidden Subgraphs,Proc. of the 1981 internat. Conf. on Convexity and Graph Theory, Israel 1981, to appear.