4-cycle properties for characterizing rectagraphs and hypercubes

Czechoslovak Mathematical Journal

Khadra Bouanane, Abdelhafid Berrachedi¹ 

关键词: hypercube;    $(0;    2)$-graph;    rectagraph;    4-cycle;    characterization;   

DOI  :  10.21136/CMJ.2017.0227-15

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  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.

【 授权许可】

Unknown