Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 11-30.
CONSTRUCTING FLAG-TRANSITIVE INCIDENCE STRUCTURES
Snježana Braić, Joško Mandić, Aljoša Šubašić and Tanja Vojković
Faculty of Science, University of Split,
21 000 Split, Croatia
e-mail: sbraic@pmfst.hr
e-mail: majo@pmfst.hr
e-mail: aljsub@pmfst.hr
e-mail: tanja@pmfst.hr
Abstract. The aim of this research is to develop efficient techniques
to construct flag-transitive incidence structures. In this paper we describe
those techniques, present the construction results and take a closer look
at how some types of flag-transitive incidence structures relate to arctransitive
graphs.
2020 Mathematics Subject Classification.
05B05, 20B25.
Key words and phrases. Incidence structures, flag-transitivity, automorphism groups,
arc-transitive graphs.
Full text (PDF) (free access)
DOI: https://doi.org/10.21857/m3v76t5g2y
References:
- M. Aschbacher, Finite geometries of type C3 with flag-transitive groups, Geom. Dedicata
16 (1984), 195-200.
MathSciNet
CrossRef
- L. M. Batten and A. Beutelspacher, The Theory of Finite Linear Spaces, Cambridge
University Press, Cambridge, 1992.
MathSciNet
CrossRef
- W. Bosma, J. J. Cannon, C. Fieker and A. Steel (eds.), Handbook of Magma functions,
Edition 2:16, 2010 (electronic).
- S. Braić, J. Mandić and T. Vučičić, Flag-transitive block designs with automorphism
group Sn wr S2, Discrete Math. 341 (2018), 2220-2230.
MathSciNet
CrossRef
- S. Braić, J. Mandić, A. Šubašić, T. Vojković and T. Vučičić,
Groups Sn × Sm in
construction of flag-transitive block designs, Glas. Mat. Ser. III 56(76) (2021), 225-240.
MathSciNet
CrossRef
- F. Buekenhout, A. Delandtsheer and J. Doyen, Finite linear spaces with flag-transitive
groups, J. Combin. Theory Ser. A. 49 (1988), 268-293.
MathSciNet
CrossRef
- C. Y. Chao, On the classification of symmetric graphs with a prime number of vertices,
Trans. Amer. Math. Soc. 158 (1971), 247-256.
MathSciNet
CrossRef
- Y. Cheng and J. Oxley, On weakly symmetric graphs of order twice a prime,
J. Combin. Theory Ser. B. 42 (1987), 196-211.
MathSciNet
CrossRef
- M. D. Conder, A. Malnič, D. Marušič and P. Potočnik, A census of semisymmetric
cubic graphs on up to 768 vertices, J. Algebraic Combin. 23 (2006), 255-294.
MathSciNet
CrossRef
- M. D. Conder, and M. Morton, Classification of trivalent symmetric graphs of small
order, Australas. J. Combin. 11 (1995), 139-150.
MathSciNet
- M. D. Conder, and R. Nedela, A refined classification of symmetric cubic graphs,
J. Algebra 322 (2009), 722-740.
MathSciNet
CrossRef
- M. D. Conder, and G. Verret, Edge-transitive graphs of small order and the answer to
a 1967 question by Folkman, Algebr. Comb. 2 (2019), 1275-1284.
MathSciNet
CrossRef
- J. Conway, and A. Ryba, The Pascal mysticum demystified, Math. Intelligencer 34 (2012),
no.3, 4-8.
MathSciNet
CrossRef
- H. S. Coxeter, Self-dual configurations and regular graphs, Bull. Amer. Math. Soc. 56
(1950), 413-455.
MathSciNet
CrossRef
- D. Z. Djokovic and G. L. Miller, Groups Acting on Regular Graphs and Group Amalgams,
in: Technical Report TR24, University of Rochester, Department of Computer
Science, Rochester, 1978.
- C. Godsil and G. Royle, Arc-Transitive Graphs, in: Algebraic Graph Theory, Springer,
New York, 2001.
MathSciNet
CrossRef
- H. Gropp, Configurations and their realization, Discrete Math. 174 (1997), 137-151.
MathSciNet
CrossRef
- https://mapmf.pmfst.unist.hr/~sbraic/BFTIS/
- F. W. Levi, Finite geometrical systems: six public lectures, University
of Calcutta, Calcutta, 1942.
MathSciNet
- P. Potočnik and S. E. Wilson,
Recipes for edge-transitive tetravalent graphs,
Art Discrete Appl. Math. 3(1) (2020), Paper No. 1.08.
MathSciNet
CrossRef
- C. E. Praeger, R. J. Wang and M. Y. Xu, Symmetric graphs of order a product of two
distinct primes, J. Combin. Theory Ser. B. 58 (1993), 299-318.
MathSciNet
CrossRef
- C. E. Praeger and M. Y. Xu, Vertex-primitive graphs of order a product of two distinct
primes, J. Combin. Theory Ser. B. 59 (1993), 245-266.
MathSciNet
CrossRef
- T. Reye, Geometrie der Lage I. 2nd ed., C. Rumpler, Hannover, 1877.
- T. Reye, Das Problem der Configurationen, Acta Math. 1(1) (1882), 93-96.
MathSciNet
CrossRef
- J. De Saedeleer, D. Leemans, M. Mixer and T. Pisanski, Core-free, rank two coset geometries
from edge-transitive bipartite graphs, Math. Slovaca 64 (2014), 991-1006.
MathSciNet
CrossRef
- J. Tits, Les groupes de Lie exceptionnels et leur interprétation géométrique, Bull. Soc.
Math. Belg. 8 (1956), 46-81.
MathSciNet
- R. J. Wang and M. Y. Xu, A classification of symmetric graphs of order 3p,
J. Combin. Theory Ser. B. 58 (1993), 197-216.
MathSciNet
CrossRef
- P.-H. Zieschang, Flag transitive automorphism groups of 2-designs with (r, λ) = 1,
J. Algebra 118 (1988), 369-375.
MathSciNet
CrossRef
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