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On 2-periodic graphs of a certain graph operator

Ivan HavelBohdan Zelinka — 2001

Discussiones Mathematicae Graph Theory

We deal with the graph operator P o w ¯ defined to be the complement of the square of a graph: P o w ¯ ( G ) = P o w ( 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...

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