On the full automorphism group of a graph. (English) Zbl 0489.05028


05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20F29 Representations of groups as automorphism groups of algebraic systems
Full Text: DOI


[1] L. Babai, On a conjecture of M. E. Watkins on graphical regular representations of groups,Compositio Math.,37 (1978), 291–296. · Zbl 0401.20004
[2] L. Babai, Finite digraphs with given regular automorphism groups,Periodica Math. Hung. to appear. · Zbl 0452.05030
[3] H. Bender, Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläßt,J. Algebra,17 (1971), 527–554. · Zbl 0237.20014
[4] H. Bender, The Brauer-Suzuki-Wall theorem,Ill. J. Math.,18 (1974), 229–235. · Zbl 0279.20014
[5] R. Brauer, M. Suzuki andG. E. Wall, A characterization of the two-dimensional unimodular projective groups over finite fields,Ill. J. Math.,2 (1958), 718–745. · Zbl 0083.25202
[6] J. K. Doyle, Graphical Frobenius representations of abstract groups,submitted.
[7] R. Frucht, A one-regular graph of degree three,Canadian J. Math.,4 (1952), 240–247. · Zbl 0046.40903
[8] C. D. Godsil, GRR’s for non-solvable groups,Proceedings of the conference on algebraic methods in combinatorics, Szeged (Hungary) 1978, Bolyai-North-Holland, 221–239.
[9] D. Gorenstein,Finite groups, Harper & Row, New York, (1968). · Zbl 0185.05701
[10] B. Huppert,Endliche Gruppen I, Springer Verlag, New York, (1967).
[11] W. Imrich andM. E. Watkins, On automorphism groups of Cayley Graphs,Per. Math. Hung.,7 (1976), 243–258. · Zbl 0351.05115
[12] D. S. Passman,Permutation Groups, W. A. Benjamin, New York, (1968).
[13] G. Sabidussi, Vertex-transitive graphs,Monat. Math.,68 (1964), 426–438. · Zbl 0136.44608
[14] J. Tate, Nilpotent quotient groups,Topology,3 (1964), 109–111. · Zbl 0125.01503
[15] M. E. Watkins, On the action of non-abelian groups on graphs,J. Combinatorial Theory,11 (1971), 95–104. · Zbl 0227.05108
[16] M. E. Watkins, Graphical regular representations of alternating, symmetric and miscellaneous small groups,Aequat. Math. 11 (1974), 40–50. · Zbl 0294.05114
[17] T. Yoshida, Character theoretic transfer,J. Algebra,52 (1978), 1–38. · Zbl 0399.20006
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