The generalized prism πG of G is the graph consisting of two copies of G, with edges between the copies determined by a permutation π acting on the vertices of G. We define a generalized Cartesian product G π H that corresponds to the Cartesian product G H when π is the identity, and the generalized prism when H is the graph K2. Burger, Mynhardt and Weakley [On the domination number of prisms o...

Abstract Given smooth manifolds $$M_1,\ldots , M_n$$ M 1 , … n (which may have a boundary or corners), manifold N modeled on locally convex spaces and $$\alpha \in ({{\mathbb {N}}}_0\cup \{\infty ...

Let y(G) be the domination number of a graph G and let G U H denote the Cartesian product of graphs G and H. We prove that y(X) = (nr= ,nr)/(2m + l), where X = C1 0 CZ 0 ... 0 C, and all nt = ICkIr 1 < k < m, are multiples of 2m + 1. The methods we use to prove this result immediately lead to an algorithm for finding minimum dominating sets of the considered graphs. Furthermore the domination n...

Radio labeling is derived from the assignment of radio frequencies (channels) to a set of transmitters. The frequencies assigned depend on the geographical distance between the transmitters: the closer two transmitters are, the greater the potential for interference between their signals. Thus when the distance between two transmitters is small, the difference in the frequencies assigned must b...

The article includes: theorems related to domains, theorems related to Cartesian products presented earlier in various articles and simplified here by substituting domains for sets and omitting the assumption that the sets involved must not be empty. Several schemes and theorems related to Fraenkel operator are given. We also redefine subset yielding functions such as the pair of elements of a ...

The purpose of this article is to define projections of ordered pairs, and to introduce triples and quadruples, and their projections. The theorems in this paper may be roughly divided into two groups: theorems describing basic properties of introduced concepts and theorems related to the regularity, analogous to those proved for ordered pairs by Cz. Byliński [1]. Cartesian products of subsets ...