论文信息 - Weakly Flag-transitive Configurations and Half-arc-transitive Graphs

Weakly Flag-transitive Configurations and Half-arc-transitive Graphs

A configuration is weakly flag-transitive if its group of automorphisms acts intransitively on flags but the group of all automorphisms and anti-automorphisms acts transitively on flags. It is shown that weakly flag-transitive configurations are in one-to-one correspondence with bipartite12-arc-transitive graphs of girth not less than 6. Several infinite families of weakly flag-transitive configurations are given via their Levi graphs. Among others an infinite family of non-self-polar weakly flag-transitive configurations is constructed. The smallest known weakly flag-transitive configuration has 27 points and the smallest known non-self-polar weakly flag-transitive configuration has 34 points.

Dragan Marusic | Tomaz Pisanski

[1] I. Bouwer. Vertex and Edge Transitive, but not 1-Transitive, Graphs , 1970, Canadian Mathematical Bulletin.

[2] H. Coxeter. Self-dual configurations and regular graphs , 1950 .

[3] W. T. Tutte. Connectivity in graphs , 1966 .

[4] H. Coxeter,et al. Generators and relations for discrete groups , 1957 .

[5] D. Robinson. A Course in the Theory of Groups , 1982 .

[6] Dragan Marusic,et al. Half-Transitive Group Actions on Finite Graphs of Valency 4 , 1998, J. Comb. Theory, Ser. B.

[7] C. Colbourn,et al. The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[8] Arthur T. White,et al. Permutation Groups and Combinatorial Structures , 1979 .

[9] Elwood S. Buffa,et al. Graph Theory with Applications , 1977 .

[10] N. Biggs. Algebraic Graph Theory , 1974 .

[11] J. A. Bondy,et al. Graph Theory with Applications , 1978 .

[12] Cheryl E. Praeger,et al. Tetravalent Graphs Admitting Half-Transitive Group Actions: Alternating Cycles , 1999, J. Comb. Theory, Ser. B.

[13] J. Folkman. Regular line-symmetric graphs , 1967 .

[14] B. Sturmfels. Computational Synthetic Geometry , 1989 .

[15] Dragan Marusic. Recent developments in half-transitive graphs , 1998, Discret. Math..