Graph bundles and Ricci-flatness

Abstract

We develop a systematical way of constructing S-Ricci flat graphs which are not Abelian Cayley via graph bundle with explicit examples. For this purpose, we prove that, with some natural constrains, a non-trivial graph bundle can not be isomorphic (as graphs) to the product of the base graph and fiber graph. It stands in clear contrast to the continuous case.

We add an assumption in the statement of Theorem 3 and 4 which was omitted in the previous version and also a new example