# 4-cycle properties for characterizing rectagraphs and hypercubes

Khadra Bouanane; Abdelhafid Berrachedi

Czechoslovak Mathematical Journal (2017)

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

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topBouanane, 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 -

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