Geodesic
On 2-periodic graphs of a certain graph operator
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 13-30.

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We deal with the graph operator Pow₂ defined to be the complement of the square of a graph: Pow₂(G) = Pow₂(G). Motivated by one of many open problems formulated in [6] we look for graphs that are 2-periodic with respect to this operator. We describe a class of bipartite graphs possessing the above mentioned property and prove that for any m,n ≥ 6, the complete bipartite graph K_m,n can be decomposed in two edge-disjoint factors from . We further show that all the incidence graphs of Desarguesian finite projective geometries belong to and find infinitely many graphs also belonging to among generalized hypercubes.
Keywords: graph operator, power and complement of a graph, Desarguesian finite projective geometry, decomposition of a complete bipartite graph, generalized hypercube 
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Havel, Ivan; Zelinka, Bohdan. On 2-periodic graphs of a certain graph operator. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 13-30. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a1/

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