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Isomorphic components of Kronecker product of bipartite graphs

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Jha P., Klavžar S., Zmazek B.

Discussiones Mathematicae Graph Theory

1997

tom 17

nr 2

301-309

Weichsel (Proc. Amer. Math. Soc. 13 (1962) 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the above condition and it is conjectured that the converse is true in general.

Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$

100%

Factor K., Langley L.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 1

51-67

The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Factor K.

1 Jha P.

1 Klavžar S.

1 Langley L.

1 Zmazek B.

1 2007

1 1997

Wyniki wyszukiwania

Isomorphic components of Kronecker product of bipartite graphs

Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$