Recent developments in half-transitive graphs

Discrete Mathematics

Volumn 182, Issue 1-3, 1998, Pages 219-231

  Marušič, Dragan ^a  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012581995     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(97)00142-8     Document Type: Article

References (28)

1. B. Alspach, D. Marušič, L. Nowitz, Constructing graphs which are 1/2-transitive, J. Austral. Math. Soc. A 56 (1994) 391-402.
2. B. Alspach, M.-Y. Xu, 1/2-arc-transitive graphs of order 3p, J. Algebraic Combin. 3 (1994) 347-355.
3. I.Z. Bouwer, Vertex and edge-transitive but not 1-transitive graphs, Canad. Math. Bull. 13 (1970) 231-237.
4. M.D.E. Conder, C.E. Praeger, Remarks on path-transitivity in finite graphs, University of Auckland Mathematics Department Research Report Series, No. 268, 1992.
5. J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985.
6. S.F. Du, M.Y. Xu, The vertex-primitive 1/2-transitive graphs with the smallest order, submitted.
7. R. Frucht, A one-regular graph, Canad. J. Math. 4 (1952) 340-347.
8. D.F. Holt, A graph which is edge transitive but not arc transitive, J. Graph Theory 5 (1981) 201-204.
9. D. Holton, Research problem 9, Discrete Math. 38 (1982) 125.
10. A. Malnič, D. Marušič, Constructing 4-valent 1/2-transitive graphs with a nonsolvable group of automorphisms, submitted.
11. 2, submitted.
12. W.A. Manning, On the order of primitive groups III, Trans. Amer. Math. Soc. 19 (1918) 127-142.
13. D. Marušič, Half-transitive group actions on finite graphs of valency 4, J. Combin. Theory Ser. B, to appear.
14. D. Marušič, R. Nedela, Maps, one-regular graphs and half-transitive graphs of valency 4, European J. Combin., to appear.
15. D. Marušič, R. Nedela, Finite graphs of valency 4 and girth 4 admitting half-transitive group actions, submitted.
16. D. Marušič, M.-Y. Xu, A 1/2-transitive graph of valency 4 with a nonsolvable group of automorphisms, J. Graph Theory 25 (1997) 133-138.
17. R. Nedela, M Škoviera, The construction of regular maps of given type with arbitrary edge width, submitted.
18. P.M. Neumann, Finite permutation groups, edge-coloured graphs and matrices, Topics in Group Theory and Computations, Proc. Summer School, University Coll., Galway, 1973, pp. 82-118, Academic Press, London, 1977.
19. C.E. Praeger, M.-Y. Xu, Vertex-primitive graphs of order a product of two distinct primes, J. Combin. Theory Ser. B 59 (1993) 245-266.
20. M. Šajna, Half-transitivity of some metacirculants, Discrete Math., submitted.
21. D.E. Taylor, M.-Y. Xu, Vertex-primitive 1/2-transitive graphs, J. Austral. Math. Soc. Ser. A 57 (1994) 113-124.
22. C. Thomassen, M.E. Watkins, Infinite vertex-transitive, edge-transitive, non 1-transitive graphs, Proc. Amer. Math. Soc. 105 (1989) 258-261.
23. W.T. Tutte, A family of cubical graphs, Proc. Cambridge Phil. Soc. 43 (1948) 459-474.
24. W.T. Tutte, Connectivity in graphs, University of Toronto Press, Toronto, 1966.
25. R.-J. Wang, Half-transitive graphs of order a product of two distinct primes, Comm. Algebra 22 (1994) 915-927.
26. H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964.
27. M.-Y. Xu, Half-transitive graphs of prime cube order, J. Algebraic Combin. 1 (1992) 275-282.
28. M.-Y. Xu, Some new results on 1/2-transitive graphs, Adv. Math. China 23 (1994) 505-516.