The articles [7], [4], [10], [9], [5], [2], [3], [1], [6], and [8] provide the notation and terminology for this paper. We adopt the following rules: X , Y denote non empty metric spaces, x1, y1, z1 denote elements of X , and x2, y2, z2 denote elements of Y . The scheme LambdaMCART deals with non empty sets A , B, C and a 4-ary functor F yielding an element of C , and states that: There exists ...

A graph is said to be S-prime if, whenever it is a subgraph of a nontrivial Cartesian product graph, it is a subgraph of one of the factors. A diagonalized Cartesian product is obtained from a Cartesian product graph by connecting two vertices of maximal distance by an additional edge. We show there that a diagonalized product of S-prime graphs is again S-prime. Klavžar et al. [Discr. Math. 244...

In this paper, we design an algorithm that, given a directed graph G and the Cartesian-product decomposition of its underlying undirected graph G̃, produces the directed Cartesian-product decomposition of G in linear time. This is the first time that the linear complexity is achieved for this problem, which has two major consequences. Firstly, it shows that the directed and undirected versions o...