Abstract
The generalized de Bruijn graph UGB (n, n2 + 1) is the graph with vertex set V = { 0, 1, . . . , n2} and the neighbor- hood N (i) of i ? V is N(i) = X(i) n Y(i) where X(i) = {in + d(mod n2 + 1) : a ? D and [(2i -MA) + (n2 + l)Z] n D = ?}, Y(i) = {(p - i)n(mod n2 + 1) : ? ? D and [(/?-2i)n+(n2+1)Z]flD = $}.Znthispuper,we shall show that the diameter of UGB (n, n2 + 1) is at most 4for n odd and n l\geq 5