Finite 2-geodesic transitive graphs of prime valency

2015/04/17 by Alice Devillers, Devillers, Alice, Wei Jin +5 · 3 citations
Engineering · Mathematics · #05E18 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1504.04422

openalex publication_date 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify non-complete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of 2-geodesics. We prove that either Γ is 2-arc transitive or the valency p satisfies p≡ 1\pmod 4, and for each such prime there is a unique graph with this property: it is a non-bipartite antipodal double cover of the complete graph K_p+1 with automorphism group PSL(2,p)× Z₂ and diameter 3.

Cited by

• On distance transitive graphs and 4-geodesic transitive graphs
• Finite s-geodesic transitive graphs under certain girths
• Geodesic transitive graphs of small valency

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