On the diameter of the generalized de Bruijn graphs UGB(n, n2+1)

The generalized de Bruijn graph UG_B(n, n²+1) is the graph with vertex set V={0, 1, ..., n²} and the neighborhood N(i) of i∈V is N(i)=X(i)∩Y(i) where X(i)={in+d(modn²+1):α∈D and [(2i-αn)+(n²+1)Z]∩D=Ø}, Y(i)={(β-i)n(modn²+1):β∈D and [(β-2i)n+(n ²+1)Z]∩D=Ø}. In this paper, we show that the diameter of UG_B(n, n²+1) is at most 4 for n odd and n⩾5