In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s ≥ 2. In particular, it is shown that, for any given integer k with k ≥ 3 and k ≠ 7, there exists a finite set ...

It would be interesting to find a vertex transitive graph whose matching polynomial has a nonsimple root. Such a graph would not have a hamiltonian path (see [1,2]) and would disprove a conjecture of ...

Our approach uses the theory of locally 𝑠-arc-transitive graphs developed by Giudici, Li, and Praeger [Trans. Amer. Math. Soc. 356 (2004), 291–317] to characterize antiflag-transitive generalized ...