The existence of unexpected automorphisms in direct product graphs

Xiaomeng Wang, Yan-Li Qin, Binzhou Xia

A pair of graphs $(\hat{I}“,\hat{I}\pounds )$ is called unstable if their direct product $\hat{I}“\times \hat{I}\pounds$ admits automorphisms not from $\mathrm{Aut}(\hat{I}“)\times \mathrm{Aut}(\hat{I}\pounds )$, and such automorphisms ar…