On Generalised Paley Graphs and Their Automorphism Groups
نویسندگان
چکیده
The generalised Paley graphs, as the name implies, are a generalisation of the Paley graphs which are well-known to be self-complementary and arc-transitive. They are defined as follows. Let F be a finite field of order p, where p is a prime, and let S be a subgroup of the multiplicative group of F, where S must have even order if p is odd. The generalised Paley graph of F relative to S has vertex set F and edges {x, y} where x − y ∈ S. Generalised Paley graphs occur as one of the basic graphs of the cyclotomic association schemes, and they also arise as examples of arc-transitive factors of homogeneous factorisations of complete graphs. In this paper, we study the automorphism groups of generalised Paley graphs, and in some cases, compute their full automorphism groups. Moreover we determine precisely when these graphs are connected and when they are isomorphic to Hamming
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