On the Diameter of the Generalized De Bruijn Graphs uGB(n, n2 + 1)

The generalized de Bruijn graph UGB (n, n2 + 1) is thegraph 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) : β ? Dand [(/β-2i)n+(n2+1)Z]flD = $}.Znthispuper,weshall show that the diameter of UGB (n, n2 + 1) is at most4for n odd and n l\geq 5