Distances and isomorphisms in 4-regular circulant graphs

We compute the Wiener index and the Hosoya polynomial of the Cayley graph of some cyclic groups, with all possible generating sets containing four elements, up to isomorphism. We find out that the order 17 is the smallest case providing two non-isomorphic 4-regular circulant graphs with the same Wiener index. Some open problems and questions are listed