Automorphisms of the double cover of a circulant graph of valency at most 7 [Elektronski vir]
Hujdurović, Ademir, 1987- ; Mitrović, Ðorđe ; Morris, Dave Witte
A graph is said to be unstable if the direct product (also called the canonical double cover of ) has automorphisms that do not come from automorphisms of its factors and . It is nontrivially ...unstable if it is unstable, connected, and non-bipartite, and no two distinct vertices of X have exactly the same neighbors. We find all of the nontrivially unstable circulant graphs of valency at most . (They come in several infinite families.) We also show that the instability of each of these graphs is explained by theorems of Steve Wilson. This is best possible, because there is a nontrivially unstable circulant graph of valency that does not satisfy the hypotheses of any of Wilson’s four instability theorems for circulant graphs.
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