## $$d$$-dimensional linear congruential graphs.(English)Zbl 0804.05048

The $$d$$-dimensional linear congruential graph is defined as follows: The vertex set is a finite $$d$$-dimensional linear space $$Z_{s_ 1} \times \cdots \times Z_{s_ d}$$ where $$Z_{s_ i}$$ is the residue group modulo $$s_ i$$. The edge set is defined by $$d$$ linear functions. This is a generalization of de Bruijn digraphs, Kautz digraphs, generalized de Bruijn digraphs, and Imase-Itoh digraphs. In this paper, the authors show that for properly selected functions, 2-dimensional linear congruential graphs generate regular, highly connected graphs.

### MSC:

 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C20 Directed graphs (digraphs), tournaments

### Keywords:

linear congruential graph; digraphs