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On 2-periodic graphs of a certain graph operator

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Havel I., Zelinka B.

Discussiones Mathematicae Graph Theory

2001

tom 21

nr 1

13-30

We deal with the graph operator $\overline{Pow₂}$ defined to be the complement of the square of a graph: $\overline{Pow₂}(G) = \overline{Pow₂(G)}$. 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 𝓖 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 𝓖. We further show that all the incidence graphs of Desarguesian finite projective geometries belong to 𝓖 and find infinitely many graphs also belonging to 𝓖 among generalized hypercubes.

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1 Discussiones Mathematicae Graph Theory

1 Havel I.

1 Zelinka B.

1 2001

Wyniki wyszukiwania

On 2-periodic graphs of a certain graph operator