Diameter lower bounds for Waring graphs and multiloop networks

AbstractWe study the diameter of Waring graphs over Zp, where p is a prime, i.e., Cayley graphs on (Zp, +) with generators of the mth powers. For fixed degree k and large p, we obtain a lower bound of order Θ(p1/φ(k)), where Θ is Euler's totient function. An analogous lower bound on the diameter of families of circulant graphs of fixed degree and given Z-rank of the generators is given