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Domatic number of graph products

Kijewska M.

Journal of Mathematics and Applications

2008

Vol. 30

71-81

A partition of V(G), all of whose classes arę dominating sets in G, is called a domatic partition of G. The maximum number of classes of a domatic partition of G is called the domatic nuraber of G. In this paper we explore the bounds for the domatic numbers of the cartesian product, the strong product and the join of two graphs. The bounds are the best possible in the sense that there exist examples for which equalities are attained.

Isomorphisms of Cartesian products of l-power series spaces

Karapinar E., Yurdakul M., Zahariuta V.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

Vol. 54, no 2

103-111

Let l be a Banach sequence space with a monotone norm [...], in which the canonical system (ei) is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products E[...](a) x E[...][b) where E[...](a) = K[...] and oE[...](b) = K[...) are finite and infinite l-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by the third author.

On the uniqueness of the decomposition of continua into Cartesian products

Rosicki W.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 3

247-250

There exist two 2-dimensional continua such that they are not homeomorphic but their Cartesian squares are homeomorphic. There exist two 2-dimensional continua such that they are not homeomorphic but their Cartesian products with 1-dimensional continuum different from an arc are homeomorphic.