We develop a machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are: (1) The product of meager/null-additive sets in the Cantor space is meager/nulladditive, respectively. (2) The product of a meager/null-additive set and a strong measure zero/strongly meager set in the Cantor space has strong measur...

We investigate graphs and hypergraphs that have (relaxed) product structures. In the class of graphs, we discuss in detail RSP-relations, a relaxation of relations fulfilling the square property and therefore of the product relation σ, that identifies the copies of the prime factors of a graph w.r.t. the Cartesian product. For K2,3-free graphs finest RSP-relations can be computed in polynomial-...

The purpose of this paper is to study the information ratio of perfect secret sharing of product of some special families of graphs. We seek to prove that the information ratio of prism graphs $Y_{n}$ are equal to $frac{7}{4}$ for any $ngeq 5$, and we will gave a partial answer to a question of Csirmaz cite{CL}. We will also study the information ratio of two other families $C_{m}times C_{n}$ a...

This paper is concerned with the bipanconnectivity of Cartesian product networks. It provides sufficient conditions for a Cartesian product network to be bipanconnected and uses this general result to re-prove existing results as regards the k-ary n-cube, due to Stewart and Xiang and to Hsieh and Lin, as well as to extend these results to multidimensional toroidal meshes.

In this paper, we provide exact value of the multiplicative version of the reciprocal degree distance and the multiplicative version of the reciprocal Gutman index of Cartesian product of complete graphs. Also, we establish sharp upper bounds for the multiplicative version of the reciprocal degree distance and multiplicative version of the reciprocal Gutman index of strong product of graphs.