2015/09/10 by Gareth A. Jones, Jones, Gareth A., Robert Jajcay +1
Computer Science · Mathematics · #05E18 (primary) #20B05 #20B20 #20B25 (secondary) #Advanced Graph Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.CO #math.GR #msc:05E18 #msc:20B05 #msc:20B20 #msc:20B25
paper · pdf · doi:10.48550/arxiv.1509.03125
arxiv created 2015/09/10 · openalex publication_date 2015/09/10 · arxiv updated 2015/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extending earlier results of Godsil and of Dobson and Malnic on Johnson graphs, we characterise those merged Johnson graphs J=J(n,k)I which are Cayley graphs, that is, which are connected and have a group of automorphisms acting regularly on the vertices. We also characterise the merged Johnson graphs which are not Cayley graphs but which have a transitive group of automorphisms with vertex-stabilisers of order 2. Even though these merged Johnson graphs are all vertex-transitive, we show that only relatively few of them are Cayley graphs or have a transitive group of automorphisms with vertex-stabilisers of order 2.