Finite 2‐Distance Transitive Graphs |
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| Authors: | Brian P Corr Wei Jin Csaba Schneider |
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| Institution: | 1. DEPARTAMENTO DE MATEMáTICA, INSTITUTO DE CIêNCIAS EXATAS, UNIVERSIDADE FEDERAL DE MINAS GERAIS, BELO HORIZONTE, MG, BRAZIL;2. SCHOOL OF STATISTICS, JIANGXI UNIVERSITY OF FINANCE AND ECONOMICS, NANCHANG, JIANGXI, P. R.CHINA;3. RESEARCH CENTER OF APPLIED STATISTICS, JIANGXI UNIVERSITY OF FINANCE AND ECONOMICS, NANCHANG, JIANGXI, P. R.CHINA |
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| Abstract: | 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  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. |
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| Keywords: | 2010 Mathematics Subject Classification 05E18 20B25 2‐distance transitive graph 2‐arc transitive graph permutation group 05E18 20B25 |
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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.