hypercube; $(0,2)$-graph; rectagraph; 4-cycle; characterization
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.
 Mulder, H. M.: The Interval Function of a Graph
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| Zbl 0446.05039
 Nieminen, J., Peltola, M., Ruotsalainen, P.: Two characterizations of hypercubes
. Electron. J. Comb. (electronic only) 18 (2011), Research Paper 97 10 pages. MR 2795778
| Zbl 1217.05195