On the classification of distance-transitive orbital graphs of overgroups of the jevons group

The Jevons group is the exponential group S₂ t S_n. It is generated by the group of all permutation (n x n)-matrices over GF(2) and the translation group on the n-dimensional vector space V_n over GF(2). For a permutation group G on V_n being an overgraph of S₂ t S_n, an orbital of G is an orbit of G in its natural action on V_n x Vn. The orbital graph associated with an orbital Г is the graph with the vertex set V_n and the edge set Г. In this paper, we classify distance-transitive orbital graphs of overgroups of the Jevons group S₂ t S_n and show that some of them are isomorphic to the following graphs: the complete graph K₂n, the complete bipartite graph K₂n-i,₂n-i, the halved (n + 1)-cube, the folded (n + 1)-cube, alternating forms graphs, the Taylor graph, the Hadamard graph.

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