4-cycle properties for characterizing rectagraphs and hypercubes

Khadra Bouanane; Abdelhafid Berrachedi

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 1, page 29-36
  • ISSN: 0011-4642

Abstract

top
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

top

Bouanane, Khadra, and Berrachedi, Abdelhafid. "4-cycle properties for characterizing rectagraphs and hypercubes." Czechoslovak Mathematical Journal 67.1 (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},
volume = {67},
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
VL - 67
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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.