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Finite 2‐Geodesic Transitive Graphs of Prime Valency
Authors:Alice Devillers  Wei Jin  Cai Heng Li  Cheryl E. Praeger
Affiliation:1. CENTRE FOR THE MATHEMATICS OF SYMMETRY AND COMPUTATION, SCHOOL OF MATHEMATICS AND STATISTICS, THE UNIVERSITY OF WESTERN AUSTRALIA, CRAWLEY, AUSTRALIA;2. SCHOOL OF STATISTICS, RESEARCH CENTRE OF APPLIED STATISTICS, JIANGXI UNIVERSITY OF FINANCE AND ECONOMICS, NANCHANG,, P.R. CHINAContract grant sponsor: NNSF (11301230), Jiangxi (GJJ14351, 20142BAB211008) and UWA (SIRF).
Abstract:We classify noncomplete 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 urn:x-wiley:03649024:media:jgt21835:jgt21835-math-0001, and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph urn:x-wiley:03649024:media:jgt21835:jgt21835-math-0002 with automorphism group urn:x-wiley:03649024:media:jgt21835:jgt21835-math-0003 and diameter 3.
Keywords:2‐geodesic transitive graph  2‐arc transitive graph  cover
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