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NEW CONSTRUCTIONS OF SELF-COMPLEMENTARY CAYLEY GRAPHS
Journal of the Australian Mathematical Society  (IF0.8),  Pub Date : 2021-01-12, DOI: 10.1017/s1446788720000488
CAI HENG LI, GUANG RAO, SHU JIAO SONG

Vertex-primitive self-complementary graphs were proved to be affine or in product action by Guralnick et al. [‘On orbital partitions and exceptionality of primitive permutation groups’, Trans. Amer. Math. Soc. 356 (2004), 4857–4872]. The product action type is known in some sense. In this paper, we provide a generic construction for the affine case and several families of new self-complementary Cayley graphs are constructed.