We extend two description logics by introducing cartesian product (CP) of concepts and roles. In SROIQ , we show how CP axioms can be reduced using other language constructs. We present a polynomial algorithm for subsumption checking in EL++ with CP axioms. We prove that the introduction of CP does not increase the complexity of reasoning tasks in both SROIQ and EL++ .

We show that every simple, (weakly) connected, possibly directed and infinite, hypergraph has a unique prime factor decomposition with respect to the (weak) Cartesian product, even if it has infinitely many factors. This generalizes previous results for graphs and undirected hypergraphs to directed and infinite hypergraphs. The proof adopts the strategy outlined by Imrich and Žerovnik for the c...

There are four standard products of graphs: the direct product, the Cartesian product, the strong product and the lexicographic product. The chromatic number turned out to be an interesting parameter on all these products, except on the Cartesian one. A survey is given on the results concerning the chromatic number of the three relevant products. Some applications of product colorings are also ...

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...

In this paper we reconstruct nontrivial connected Cartesian product graphs from single vertex deleted subgraphs. We show that all one-vertex extensions of a given connected graph H, nite or innnite, to a nontrivial Cartesian product are isomorphic.

Explicit expressions of the restricted edge connectivity of the Cartesian product of regular graphs are presented; some sufficient conditions for regular Cartesian product graphs to be maximally or super restricted edge connected are obtained as a result.

Equivalence relations on the edge set of a graph G that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable partitions on the vertex set of G, which in turn give rise to quotient graphs that can have a rich product structure even if G itself is prime.