Abstract
Vertex-transitive graphs whose order is a product of two primes with a primitive automorphism group containing no imprimitive subgroup are classified. Combined with the results of [15] a complete classification of all vertex-transitive graphs whose order is a product of two primes is thus obtained (Theorem 2.1).
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References
B. Alspach, andT. D. Parsons: A construction for vertex-transitive graphs,Canad. J. Math. 34 (1982), 307–318.
N. Biggs, andA. T. White:Permutation groups and combinatorial structures, Cambridge University Press, 1979.
J. van Bon andA. M. Cohen: Linear groups and distance-transitive graphs,Europ. J. Combinatorics 10 (1989), 399–411.
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, andR. A. Wilson:Atlas of finite groups, Clarendon Press, Oxford, 1985.
I. A. Faradzev, andA. A. Ivanov: Distance-transitive representation of groups withPSL 2 (q)≤G≤PΓL 2 (q),Europ. J. Combin. 11 (1990), 347–356.
R. Frucht: How to describe a graph,Ann. N. Y. Acad. Sci. 175 (1970), 159–167.
X. L. Hubaut: Strongly regular graphs,Discrete Math. 13 (1975), 357–381.
B. Huppert:Endliche Gruppen, I, Springer-Verlag, Berlin, 1967.
A. A. Ivanov, M. Kh. Klin, S. V. Tsaranov, andS. V. Shpektorov: On the problem of computation of subdegrees of transitive permutation groups,Russian Math. Survey 38, no. 6 (1983), 123–124.
M. W. Liebeck, andJ. Saxl: Primitive permutation groups containing an element of large prime order,J. London Math. Soc. (2)31 (1985), 237–249.
L. Lovász: Problem 11,Combinatorial Structures and Their Applications, ed. R. Guy, H. Hanani, N. Sauer and J. Schönheim, Gordon and Breach, New York, 1970, 497.
D. Marušič: On vertex symmetric digraphs,Discrete Math. 36 (1981), 69–81.
D. Marušič: Hamiltonicity of vertex-transitivepq-graphs,Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity, ed. J. Nešetřil and M. Fiedler, 1992 Elsevier Science Publishers, 209–212.
D. Marušič, andR. Scapellato: Imprimitive representations ofSL (2,2k),J. Combin. Theory, B 58 (1993), 46–57.
D. Marušič, andR. Scapellato: Characterizing vertex-transitivepq-graphs with an imprimitive automorphism subgroup,J. Graph Theory 16 (1992), 375–387.
D. Marušič andR. Scapellato: A class of non-Cayley vertex-transitive graphs associated withPSL(2, p), Discrete Math.,109 (1992), 161–170.
D. Marušič, andR. Scapellato: A class of graphs arising from the action ofPSL(2, q 2) on cosets ofPGL(2, q),Discrete Math., to appear.
D. Marušič, andR. Scapellato: Permutation groups with conjugacy complete stabilizers,Discrete Math., to appear.
C. Praeger, H. J. Wang, andM. Y. Xu: Symmetric graphs of order a product of two distinct primes,J. Combin. Theory, B 58 (1993), 299–316.
C. Praeger, andM. Y. Xu: Vertex primitive graphs of order a product of two distinct primes,J. Combin. Theory, B, to appear.
T. Tchuda: Combinatorial-geometric characterization of some primitive representations of the groupsPSL n (q), n=2,3, PhD Thesis, Kiev, 1986 (in Russian).
H. Wielandt:Permutation groups, Academic Press, New York, 1966.
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Supported in part by the Research Council of Slovenia
Supported in part by the Italian Ministry of Research (MURST)
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Marušič, D., Scapellato, R. Classifying vertex-transitive graphs whose order is a product of two primes. Combinatorica 14, 187–201 (1994). https://doi.org/10.1007/BF01215350
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DOI: https://doi.org/10.1007/BF01215350