Regular embeddings of canonical double coverings of graphs
Journal of Combinatorial Theory Series B
Proofs from THE BOOK
Regular embeddings of Kn,n where n is a power of 2. I: Metacyclic case
European Journal of Combinatorics
Regular embeddings of Kn,n where n is an odd prime power
European Journal of Combinatorics
Vertex transitive embeddings of complete graphs
Journal of Combinatorial Theory Series B
Classification of primer hypermaps with a prime number of hyperfaces
European Journal of Combinatorics
The Automorphism Group of a Johnson Graph
SIAM Journal on Discrete Mathematics
Characterisations and Galois conjugacy of generalised Paley maps
Journal of Combinatorial Theory Series B
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The merged Johnson graph J(n, m)I is the union of the distance i graphs J(n, m)i of the Johnson graph J(n, m) for i ∈ I, where Ø ≠ I ⊆ {1,...,m} and 2 ≤ m ≤ n/2. We find the automorphism groups of these graphs, and deduce that their only regular embedding in an orientable surface is the octahedral map on the sphere for J(4, 2)1, and that they have just six non-orientable regular embeddings. This yields classifications of the regular embeddings of the line graphs L(Kn) = J(n, 2)1 of complete graphs, their complements L(Kn) = J(n, 2)2, and the odd graphs Om+1 = J(2m + 1, m)m.