In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...

Datalog systems evaluate joins over arithmetic (in)equalities as a naive generate-and-test of Cartesian products. We exploit aggregates in a source-to-source transformation to reduce the size of Cartesian products and to improve performance. Our approach approximates the well-known propagation technique from Constraint Programming. Experimental evaluation shows good run time speed-ups on a rang...

This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local approach that covers a graph by small subgraphs, so-called partial star products, and then utilizes this information to derive the global factors and an embeddin...

This article deenes ordered n-tuples, projections and Cartesian products for n = 5. We prove many theorems concerning the basic properties of the n-tuples and Cartesian products that may be utilized in several further, more challenging applications. A few of these theorems are a strightforward consequence of the regularity axiom. The article originated as an upgrade of the article 3]. The artic...