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Finite 2‐Distance Transitive Graphs
Author(s) -
Corr Brian P.,
Jin Wei,
Schneider Csaba
Publication year - 2017
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.22112
Subject(s) - combinatorics , mathematics , transitive relation , valency , transitive reduction , vertex (graph theory) , discrete mathematics , symmetric graph , indifference graph , graph , line graph , voltage graph , philosophy , linguistics
A noncomplete graph Γ is said to be ( G , 2)‐distance transitive if G is a subgroup of the automorphism group of Γ that is transitive on the vertex set of Γ, and for any vertex u of Γ, the stabilizer G u is transitive on the sets of vertices at distances 1 and 2 from u . This article investigates the family of ( G , 2)‐distance transitive graphs that are not ( G , 2)‐arc transitive. Our main result is the classification of such graphs of valency not greater than 5. We also prove several results about ( G , 2)‐distance transitive, but not ( G , 2)‐arc transitive graphs of girth 4.