Connectivity of Imase and Itoh digraphs

An important problem in the design of efficient interconnection networks consists of finding digraphs with a minimal diameter for a given number of nodes n and a given degree d. The best family known at present, denoted by G(n,d), has been proposed by Imase and Itoh, ibid., vol.C-32, p.782-4 (1983). Its vertex set is the set of integers modulo n and its arc set A is defined as A={(x,y)/y≡-dx-a , 1⩽a⩽d}. The authors determine the connectivity of these digraphs, which proves that they are highly reliable. More precisely, we show that provided that the diameter is greater than 4, the connectivity of G(n,d) is d if n=k(d+1) and gcd(n,d)>1, and d-1 otherwise