Isomorphic components of Kronecker product of bipartite graphs | Zendy

Pranava K. Jha | Zendy; Sandi Klavžar | Zendy; Blaž Zmazek | Zendy

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Isomorphic components of Kronecker product of bipartite graphs

Author(s) -

Pranava K. Jha,

Sandi Klavžar,

Blaž Zmazek

Publication year - 1997

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1057

Subject(s) - mathematics , bipartite graph , combinatorics , kronecker product , product (mathematics) , complete bipartite graph , kronecker delta , discrete mathematics , graph , geometry , physics , quantum mechanics

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. Math. Subj. Class. (1991): 05C60 Key terms: Kronecker product, bipartite graphs, graph isomorphism ∗This work was supported in part by the Ministry of Science and Technology of Slovenia under the grants P1-0206-101 and J1-7036.

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