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Isomorphic components of Kronecker product of bipartite graphs

100%
Jha P., Klavžar S., Zmazek B.
Discussiones Mathematicae Graph Theory
|
1997
|
tom 17
|
nr 2
301-309
EN
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.
2
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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
EN
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.
3
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Estimation of the Kronecker and products of two mean vectors in multivariate analysis

88%
Neudecker H., Trenkler G.
Discussiones Mathematicae Probability and Statistics
|
2005
|
tom 25
|
nr 2
207-215
EN
In this paper the Kronecker and inner products of mean vectorsof two different populations are considered. Using the generalized jackknife approach, estimators for these products are constructed which turn out to be unbiased, provided one can assume multinormal distribution.
4
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Union of Distance Magic Graphs

63%
Cichacz S., Nikodem M.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 37
|
nr 1
239-249
EN
A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ from V to the set {1, . . . , n} such that the weight w(x) = ∑y∈NG(x) ℓ(y) of every vertex x ∈ V is equal to the same element μ, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.
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