Diameter lower bounds for Waring graphs and multiloop networks

Abstract

We study the diameter of Waring graphs over Z_p, where p is a prime, i.e., Cayley graphs on (Z_p, +) with generators of the mth powers. For fixed degree k and large p, we obtain a lower bound of order Θ(p^1/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.