Let k ≥ 3 be a positive odd integer and q be a power of a prime. In this paper we give an explicit construction of a q–regular bipartite graph on v = 2q vertices with girth g ≥ k + 5. The constructed graph is the incidence graph of a flag–transitive semiplane. For any positive integer t we also give an example of a q = 2–regular bipartite graph on v = 2q vertices with girth g ≥ k + 5 which is b...

This article is a contribution to the study of block-transitive automorphism groups of 2-(v, k, 1) block designs. Let D be a 2-(v, k, 1) design admitting a block-transitive, pointprimitive but not flag-transitive automorphism group G. Let kr = (k, v − 1) and q = p f for prime p. In this paper we prove that if G and D are as above and q > (3(krk − kr + 1)f) , then G does not admit a simple group...

This paper is a contribution to the classification of flag-transitive 4- $$(v,k,\lambda )$$ designs. Let $$\mathcal D=({\mathcal {P}}, {\mathcal {B}})$$ be $$(q+1,k,\lambda design with $$\lambda \ge 5$$ and $$q+1>k>4$$ , $$G=PSL(2,q)$$ automorphism group D$$ $$G_x$$ stabilizer point $$x\in {P}}$$ $$G_B$$ setwise block $$B\in {B}}$$ . Using fact that must one twelve kinds subgroups PSL(2, q), up...

The classification of finite flag-transitive linear spaces, obtained by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl [20] at the end of the eighties, gave new impulse to the program of classifying various classes of locally finite flag-transitive geometries belonging to diagrams obtained from a Coxeter diagram by putting a label L or L∗ on some (possibly, all) of the single-bond ...

Let $${\mathcal {D}}$$ be a nontrivial 3-(v, k, 1) design admitting block-transitive group G of automorphisms. A recent work Gan and the second author asserts that is either affine or almost simple. In this paper, it proved if simple with socle an alternating group, then unique 3-(10, 4, design, $$G=\textrm{PGL}(2,9)$$ , $$\textrm{M}_{10}$$ $$\textrm{Aut}(\textrm{A}_6 )=\textrm{S}_6:\textrm{Z}_...