Line graphs and 2-geodesic transitivity

2012/01/20 by Alice Devillers, Devillers, Alice, Wei Jin +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1201.4297

openalex publication_date 2012/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a graph Γ, a positive integer s and a subgroup G≤ \Aut(Γ), we prove that G is transitive on the set of s-arcs of Γ if and only if Γ has girth at least 2(s-1) and G is transitive on the set of (s-1)-geodesics of its line graph. As applications, we first prove that the only non-complete locally cyclic 2-geodesic transitive graphs are the complete multipartite graph K_3[2] and the icosahedron. Secondly we classify 2-geodesic transitive graphs of valency 4 and girth 3, and determine which of them are geodesic transitive.

Related

• On distance, geodesic and arc transitivity of graphs
• Two-geodesic transitive graphs of order pⁿ with n≤3
• On distance transitive graphs and 4-geodesic transitive graphs
• Finite s-geodesic transitive graphs under certain girths
• Finite 2-geodesic transitive graphs of prime valency