2019/04/02 by Wei Jin, Cheryl E. Praeger, Jin, Wei +1
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1904.01204
openalex publication_date 2019/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify all the 2-arc-transitive strongly regular graphs, and use this classification to study the family of finite (G,3)-geodesic-transitive graphs of girth 4 or 5 for some group G of automorphisms. For this application we first give a reduction result on the latter family of graphs: let N be a normal subgroup of G which has at least 3 orbits on vertices. We show that Γ is a cover of its quotient ΓN modulo the N-orbits, and that either ΓN is (G/N,3)-geodesic-transitive of the same girth as Γ, or ΓN is a (G/N,2)-arc-transitive strongly regular graph, or ΓN is a complete graph with G/N acting 3-transitively on vertices. The classification of 2-arc-transitive strongly regular graphs allows us to characterise the (G,3)-geodesic-transitive covers Γ when ΓN is complete or strongly regular.