Frontiers of Mathematics in China >
Pentavalent vertex-transitive diameter two graphs
Received date: 26 May 2015
Accepted date: 08 Oct 2016
Published date: 20 Feb 2017
Copyright
We classify the family of pentavalent vertex-transitive graphs with diameter 2. Suppose that the automorphism group of is transitive on the set of ordered distance 2 vertex pairs. Then we show that either is distance-transitive or is one of .
Key words: vertex-transitive graph; diameter; automorphism group
Wei JIN . Pentavalent vertex-transitive diameter two graphs[J]. Frontiers of Mathematics in China, 2017 , 12(2) : 377 -388 . DOI: 10.1007/s11464-016-0617-9
1 |
Amarra C, Giudici M, Praeger C E. Quotient-complete arc-transitive graphs. European J Combin, 2012, 33: 1857–1881
|
2 |
Amarra C, Giudici M, Praeger C E. Symmetric diameter two graphs with affine-type vertex-quasiprimitive automorphism group. Des Codes Cryptogr, 2013, 68: 127–139
|
3 |
Brouwer A E, Cohen A M, Neumaier A. Distance-Regular Graphs. Berlin: Springer-Verlag, 1989
|
4 |
Cameron P J. Permutation Groups. London Math Soc Stud Texts, Vol 45. Cambridge: Cambridge Univ Press, 1999
|
5 |
Cheng Y, Oxley J. On weakly symmetric graphs of order twice a prime. J Combin Theory Ser B, 1987, 42: 196–211
|
6 |
Devillers A. A classi_cation of _nite partial linear spaces with a rank 3 automorphism group of grid type. European J Combin, 2008, 29: 268–272
|
7 |
Devillers A, Giudici M, Li C H, Pearce G, Praeger C E. On imprimitive rank 3 permutation groups. J Lond Math Soc, 2011, 84: 649–669
|
8 |
Devillers A, Jin W, Li C H, Praeger C E. Local 2-geodesic transitivity and clique graphs. J Combin Theory Ser A, 2013, 120: 500–508
|
9 |
Devillers A, Jin W, Li C H, Praeger C E. On normal 2-geodesic transitive Cayley graphs. J Algebraic Combin, 2014, 39: 903–918
|
10 |
0. Dixon J D, Mortimer B. Permutation Groups. New York: Springer, 1996
|
11 |
Gorenstein D. Finite Simple Groups|An Introduction to Their Classi_cation. New York: Plenum Press, 1982
|
12 |
Hestenes M D, Higman D G. Rank 3 groups and strongly regular graphs. SIAM-AMS Proc, 1971, 4: 141–159
|
13 |
Jin W. Vertex-transitive graphs of diameter 2. Preprint
|
14 |
Kov_acs I. Classifying arc-transitive circulants. J Algebraic Combin, 2004, 20: 353–358
|
15 |
Kwak J H, Oh J M. One-regular normal Cayley graphs on dihedral groups of valency 4 or 6 with cyclic vertex stabilizer. Acta Math Sin (Engl Ser), 2006, 22: 1305–1320
|
16 |
Li C H. Permutation groups with a cyclic regular subgroup and arc transitive circulants. J Algebraic Combin, 2005, 21: 131–136
|
17 |
Li C H, Pan J M. Finite 2-arc-transitive abelian Cayley graphs. European J Combin, 2008, 29: 148–158
|
18 |
Mckay B, Praeger C E. Vertex-transitive graphs which are not Cayley graphs. J Aust Math Soc (A), 1994, 56: 53–63
|
19 |
Morris J, Praeger C E, Spiga P. Strongly regular edge-transitive graphs. Ars Math Contemp, 2009, 2: 137–155
|
20 |
Wang R J, Xu M Y. A classi_cation of symmetric graphs of order 3p:J Combin Theory Ser B, 1993, 58: 197–216
|
21 |
Wielandt H. Finite Permutation Groups. New York: Academic Press, 1964
|
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