Absorbant of generalized de Bruijn digraphs

The generalized de Bruijn digraph GB(n, d) has good properties as an interconnection network topology. The resource location problem in an interconnection network is one of the facility location problems. Finding absorbants of a digraph corresponds to solving a kind of resource location problem. In this paper, we establish bounds on the absorbant number for GB(n, d), and we give some sufficient conditions for the absorbant number of GB(n, d) to achieve the bounds. When d divides n, the extremal digraphs achieving the upper bound are characterized by determining their absorbants.