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Isomorphic components of Kronecker product of bipartite graphs

Pranava K. Jha;  Sandi Klavžar;  Blaž Zmazek — 1997

Discussiones Mathematicae Graph Theory

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.

Median and quasi-median direct products of graphs

Boštjan Brešar;  Pranava K. Jha;  Sandi Klavžar;  Blaž Zmazek — 2005

Discussiones Mathematicae Graph Theory

Median graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of G×P₃ is median if and only if G is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form G×K₂ are proved, and it is shown that the only nonbipartite quasi-median direct product is K₃×K₃.

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