On centrally symmetric graphs

Manfred Stern

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 1, page 25-28
  • ISSN: 0862-7959

Abstract

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In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices.

How to cite

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Stern, Manfred. "On centrally symmetric graphs." Mathematica Bohemica 121.1 (1996): 25-28. <http://eudml.org/doc/247987>.

@article{Stern1996,
abstract = {In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices.},
author = {Stern, Manfred},
journal = {Mathematica Bohemica},
keywords = {covering graph; symmetric graph; centrally symmetric lattice; graded lattice; strong lattice; semimodular lattice; covering graph; symmetric graph; centrally symmetric lattice; graded lattice; strong lattice},
language = {eng},
number = {1},
pages = {25-28},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On centrally symmetric graphs},
url = {http://eudml.org/doc/247987},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Stern, Manfred
TI - On centrally symmetric graphs
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 1
SP - 25
EP - 28
AB - In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices.
LA - eng
KW - covering graph; symmetric graph; centrally symmetric lattice; graded lattice; strong lattice; semimodular lattice; covering graph; symmetric graph; centrally symmetric lattice; graded lattice; strong lattice
UR - http://eudml.org/doc/247987
ER -

References

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  1. P. Crawley, R. P. Dilworth, Algebraic Theory of Lattices, Prentice Hall, Englewood Cliffs, New Jersey, 1973. (1973) Zbl0494.06001
  2. D. Duffus, I. Rival, 10.1016/0012-365X(77)90029-2, Discrete Math. 19 (1977), 139-158. (1977) Zbl0372.06005MR0543829DOI10.1016/0012-365X(77)90029-2
  3. U. Faigle, 10.1016/0095-8956(80)90054-4, J. Combin. Theory Ser. B 28 (1977), 26-51. (1977) MR0565509DOI10.1016/0095-8956(80)90054-4
  4. E. Gedeonová, Lattices whose covering graphs are S-graphs, Colloq. Math. Soc. János Bolyai 33 (1980), 407-435. (1980) MR0724274
  5. E. Gedeonová, Lattices with centrally symmetric covering graphs, Proc. Klagenfurt Conf. June 10-13, 1982, Contributions to General Algebra 2. Verlag Hölder-Pichler-Tempsky, Wien, 1983, pp. 107-113. (1982) MR0721649
  6. G. Grätzer, General Lattice Theory, Birkhäuser Verlag, Basel, 1978. (1978) MR0504338
  7. A. Kotzig, Centrally symmetric graphs, Czechoslovak Math. J. 18 (1968), 606-615. (In Russian.) (1968) MR0237376
  8. J. P. S. Kung, 10.1007/BF00334848, Order 2, 105-112. Zbl0582.06008MR0815856DOI10.1007/BF00334848
  9. K. Reuter, 10.1007/BF02170062, Acta Math. Hung. 53, 119-127. Zbl0675.06003MR0987044DOI10.1007/BF02170062
  10. M. Stern, Semimodular Lattices, B.G.Teubner Verlagsgesellschaft, Stuttgart und Leipzig, 1991. (1991) Zbl0743.06008MR1164868
  11. M. Stern, 10.1016/0012-365X(91)90220-V, Discrete Math. 93 (1991), 97-100. (1991) Zbl0759.06006MR1141266DOI10.1016/0012-365X(91)90220-V
  12. B. Zelinka, Centrally symmetric Hasse diagrams of finite modular lattices, Czechoslovak Math. J. 20 (1970), 81-83. (1970) Zbl0194.32601MR0255441

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