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Isomorphic components of direct products of bipartite graphs

100%

Hammack R.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 2

231-248

A standard result states the direct product of two connected bipartite graphs has exactly two components. Jha, Klavžar and Zmazek proved that if one of the factors admits an automorphism that interchanges partite sets, then the components are isomorphic. They conjectured the converse to be true. We prove the converse holds if the factors are square-free. Further, we present a matrix-theoretic conjecture that, if proved, would prove the general case of the converse; if refuted, it would produce a counterexample.

Centers of n-fold tensor products of graphs

63%

Bendall S., Hammack R.

Discussiones Mathematicae Graph Theory

2004

tom 24

nr 3

491-501

Formulas for vertex eccentricity and radius for the n-fold tensor product $G = ⊗_{i=1} ⁿG_i$ of n arbitrary simple graphs $G_i$ are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with $V_i ⊆ V(G_i)$.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Hammack R.

1 Bendall S.

1 2006

1 2004

Wyniki wyszukiwania

Isomorphic components of direct products of bipartite graphs

Centers of n-fold tensor products of graphs