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  • 1 I. A. E Université Jean Moulin (Lyon 3) B. P. 0638 69239 Lyon Cedex 02 France
  • | 2 Mathematics Department Syracuse University 13244-1150 Syracuse New York USA
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Let t be an infinite graph, let p be a double ray in t, and letd anddp denote the distance functions in t and in p, respectively. One calls p anaxis ifd(x,y)=d p (x,y) and aquasi-axis if lim infd(x,y)/d p (x,y)>0 asx, y range over the vertex set of p andd p (x,y)?8. The present paper brings together in greater generality results of R. Halin concerning invariance of double rays under the action of translations (i.e., graph automorphisms all of whose vertex-orbits are infinite) and results of M. E. Watkins concerning existence of axes in locally finite graphs. It is shown that if a is a translation whose directionD(a) is a thin end, then there exists an axis inD(a) andD(a-1) invariant under ar for somer not exceeding the maximum number of disjoint rays inD(a).The thinness ofD(a) is necessary. Further results give necessary conditions and sufficient conditions for a translation to leave invariant a quasi-axis.

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  • Impact Factor (2019): 0.693
  • Scimago Journal Rank (2019): 0.412
  • SJR Hirsch-Index (2019): 20
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.664
  • Scimago Journal Rank (2018): 0.412
  • SJR Hirsch-Index (2018): 19
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

Periodica Mathematica Hungarica
Language English
Size B5
Year of
per Year
per Year
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)