Automorphisms of the double cover of a circulant graph of valency at most 7

Abstract

A graph X is said to be unstable if the direct product X×K 2 (also called the canonical double cover of X) has automorphisms that do not come from automorphisms of its factors X and K 2 . It is nontrivially unstable if it is unstable, connected, and non-bipartite, and no two distinct vertices of X have exactly the same neighbors.