There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with “small” graphs. Let H be the 5-vertex graph defined from K5 by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H ×Pn and H ×Cn, showing that in the general case the corresponding crossing numbers are 3n−1...

This paper concerns finite, edge-transitive direct and strong products, as well as infinite weak Cartesian products. We prove that the direct product of two connected, non-bipartite graphs is edge-transitive if and only if both factors are edgetransitive and at least one is arc-transitive, or one factor is edge-transitive and the other is a complete graph with loops at each vertex. Also, a stro...

This paper provides an algebraic characterization of mathematical structures formed by cartesian products of fuzzy relations with sup-min composition. A simple proof of a representation theorem for Boolean relation algebras satisfying Tarski rule and point axiom was given by G. Schmidt and T. Strohlein, and cartesian products of Boolean relation algebras were investigated by B. J onsson and A....

Rewriting of conjunctive queries using views has many applications in database and data integration. We investigate ways to improve performance of rewriting and propose a new algorithm which has two phases. In the first phase, similar to Minicon, we find mapping information, which we call coverages, from subgoals in the query to subgoals in view, and assign positive integers (< 2) as identifier...

We study direct sums of structures with a one element subuniverse. We give a characterization of direct sums reminescent to that of inner products of groups. The strict refinement property is adapted to direct sums and to restricted Cartesian products of graphs. If a structure has the strict refinement property (for direct products), it has the strict refinement property for direct sums. Connec...

In this paper Cartesian, direct and strong Cartesian product of hypergraphs are investigated. A new concept named the adjacency function is defined on hypergraphs. This definition leads to distinct adjacency and Laplacian matrices for a hypergraph and makes it possible to express it in an algebraic form. Variable adjacency functions on hypergraphs result in generation of dynamic graph products ...