4-cycle properties for characterizing rectagraphs and hypercubes

Khadra Bouanane; Abdelhafid Berrachedi

Czechoslovak Mathematical Journal (2017)

  • Issue: 1, page 29-36
  • ISSN: 0011-4642

Abstract

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A ( 0 , 2 ) -graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of ( 0 , λ ) -graphs introduced by Mulder in 1979. A rectagraph, well known in diagram geometry, is a triangle-free ( 0 , 2 ) -graph. ( 0 , 2 ) -graphs include hypercubes, folded cube graphs and some particular graphs such as icosahedral graph, Shrikhande graph, Klein graph, Gewirtz graph, etc. In this paper, we give some local properties of 4-cycles in ( 0 , λ ) -graphs and more specifically in ( 0 , 2 ) -graphs, leading to new characterizations of rectagraphs and hypercubes.

How to cite

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Bouanane, Khadra, and Berrachedi, Abdelhafid. "4-cycle properties for characterizing rectagraphs and hypercubes." Czechoslovak Mathematical Journal (2017): 29-36. <http://eudml.org/doc/287868>.

@article{Bouanane2017,
abstract = {A $(0,2)$-graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of $(0,\lambda )$-graphs introduced by Mulder in 1979. A rectagraph, well known in diagram geometry, is a triangle-free $(0,2)$-graph. $(0,2)$-graphs include hypercubes, folded cube graphs and some particular graphs such as icosahedral graph, Shrikhande graph, Klein graph, Gewirtz graph, etc. In this paper, we give some local properties of 4-cycles in $(0,\lambda )$-graphs and more specifically in $(0,2)$-graphs, leading to new characterizations of rectagraphs and hypercubes.},
author = {Bouanane, Khadra, Berrachedi, Abdelhafid},
journal = {Czechoslovak Mathematical Journal},
keywords = {hypercube; $(0,2)$-graph; rectagraph; 4-cycle; characterization},
language = {eng},
number = {1},
pages = {29-36},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {4-cycle properties for characterizing rectagraphs and hypercubes},
url = {http://eudml.org/doc/287868},
year = {2017},
}

TY - JOUR
AU - Bouanane, Khadra
AU - Berrachedi, Abdelhafid
TI - 4-cycle properties for characterizing rectagraphs and hypercubes
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 29
EP - 36
AB - A $(0,2)$-graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of $(0,\lambda )$-graphs introduced by Mulder in 1979. A rectagraph, well known in diagram geometry, is a triangle-free $(0,2)$-graph. $(0,2)$-graphs include hypercubes, folded cube graphs and some particular graphs such as icosahedral graph, Shrikhande graph, Klein graph, Gewirtz graph, etc. In this paper, we give some local properties of 4-cycles in $(0,\lambda )$-graphs and more specifically in $(0,2)$-graphs, leading to new characterizations of rectagraphs and hypercubes.
LA - eng
KW - hypercube; $(0,2)$-graph; rectagraph; 4-cycle; characterization
UR - http://eudml.org/doc/287868
ER -

References

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  1. Berrachedi, A., Mollard, M., 10.1016/S0012-365X(99)00063-1, Discrete Math. 208-209 (1999), 71-75. (1999) Zbl0933.05133MR1725521DOI10.1016/S0012-365X(99)00063-1
  2. Brouwer, A. E., 10.1016/j.jcta.2006.03.023, J. Comb. Theory Ser. A 113 (2006), 1636-1645. (2006) Zbl1105.05009MR2269544DOI10.1016/j.jcta.2006.03.023
  3. Brouwer, A. E., Östergård, P. R. J., 10.1016/j.disc.2008.07.037, Discrete Math. 309 (2009), 532-547. (2009) Zbl1194.05129MR2499006DOI10.1016/j.disc.2008.07.037
  4. Burosch, G., Havel, I., Laborde, J.-M., 10.1016/0012-365X(92)90696-D, Discrete Math. 110 (1992), 9-16. (1992) Zbl0768.05033MR1197441DOI10.1016/0012-365X(92)90696-D
  5. Laborde, J.-M., Hebbare, S. P. Rao, 10.1016/0012-365X(82)90139-X, Discrete Math. 39 (1982), 161-166. (1982) Zbl0482.05033MR0675861DOI10.1016/0012-365X(82)90139-X
  6. Mulder, H. M., 10.1016/0012-365X(79)90095-5, Discrete Math. 28 (1979), 179-188. (1979) Zbl0418.05034MR0546651DOI10.1016/0012-365X(79)90095-5
  7. Mulder, H. M., The Interval Function of a Graph, Mathematical Centre Tracts 132, Mathematisch Centrum, Amsterdam (1980). (1980) Zbl0446.05039MR0605838
  8. Mulder, H. M., 10.1016/0012-365X(82)90021-8, Discrete Math. 41 (1982), 253-269. (1982) Zbl0542.05051MR0676887DOI10.1016/0012-365X(82)90021-8
  9. Neumaier, A., 10.1016/S0304-0208(08)73275-4, Ann. Discrete Math. 15 (1982), 305-318. (1982) Zbl0491.05033MR0772605DOI10.1016/S0304-0208(08)73275-4
  10. Nieminen, J., Peltola, M., Ruotsalainen, P., Two characterizations of hypercubes, Electron. J. Comb. (electronic only) 18 (2011), Research Paper 97 10 pages. (2011) Zbl1217.05195MR2795778
  11. Sabidussi, G., 10.1007/BF01162967, Math. Z. 72 (1960), 446-457. (1960) Zbl0093.37603MR0209177DOI10.1007/BF01162967

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