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Finite 2‐Geodesic Transitive Graphs of Prime Valency
Author(s) -
Devillers Alice,
Jin Wei,
Li Cai Heng,
Praeger Cheryl E.
Publication year - 2015
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21835
Subject(s) - mathematics , valency , combinatorics , antipodal point , transitive relation , automorphism group , discrete mathematics , prime (order theory) , automorphism , edge transitive graph , digraph , graph , line graph , graph power , philosophy , linguistics , geometry
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 p ≡ 1 ( mod 4 ) , and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph K p + 1with automorphism group P S L ( 2 , p ) × Z 2and diameter 3.
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