Vertex-Transitive Non-Cayley Graphs with Arbitrarily Large Vertex-Stabilizer
Marston D.E. Conder
and Cameron G. Walker
DOI: 10.1023/A:1008687226819
Abstract
A construction is given for an infinite family { p < 2 2 n + 2 p < 2^{2^n + 2} . The construction uses Sierpinski”s gasket to produce generating permutations for the vertex-stabilizer (a large 2-group).
Pages: 29–38
Keywords: symmetric graph; vertex-transitive; arc-transitive
Full Text: PDF
References
1. Marston Conder, “An infinite family of 5-arc-transitive cubic graphs,” Ars Combinatoria 25A (1988), 95-108.
2. Marston Conder and Peter Lorimer, “Automorphism groups of symmetric graphs of valency 3,” J. Combinatorial Theory Ser. B 47 (1989), 60-72.
3. B. Huppert, Endliche Gruppen I, Springer-Verlag, 1983.
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5. H.-O. Peitgen, H. J\ddot urgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, 1992.
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8. Richard Weiss, “s-Transitive graphs,” in Algebraic Methods in Graph Theory (Coll. Math. Soc. János Bolyai) 25 (1984), 827-847.
9. Helmut Wielandt, Finite Permutation Groups, Academic Press, New York, 1964.
2. Marston Conder and Peter Lorimer, “Automorphism groups of symmetric graphs of valency 3,” J. Combinatorial Theory Ser. B 47 (1989), 60-72.
3. B. Huppert, Endliche Gruppen I, Springer-Verlag, 1983.
4. R.C. Miller, “The trivalent symmetric graphs of girth at most 6,” J. Combinatorial Theory Ser. B 10 (1971), 163-182.
5. H.-O. Peitgen, H. J\ddot urgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, 1992.
6. C.E. Praeger, “Finite primitive permutation groups: A survey,” Groups-Canberra 1989 (Springer Lecture Notes in Mathematics), 1456 (1990), 63-84.
7. C.E. Praeger and M.Y. Xu, “A characterisation of a class of symmetric graphs of twice prime valency,” European J. Combinatorics 10 (1989), 91-102.
8. Richard Weiss, “s-Transitive graphs,” in Algebraic Methods in Graph Theory (Coll. Math. Soc. János Bolyai) 25 (1984), 827-847.
9. Helmut Wielandt, Finite Permutation Groups, Academic Press, New York, 1964.