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...

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

Let ? be a finite, undirected, connected, simple graph. We say that matching M is permutable m -matching if contains edges and the subgroup of Aut ( ) fixes setwise allows to permuted in any fashion. A 2-transitive stabilizer can map ordered pair distinct other . provide constructions graphs with matching; we show that, an arc-transitive graph for ? 4 , then degree at least ; and, when sufficie...

Let Γ be a finite X-symmetric graph with a nontrivial Xinvariant partition B on V (Γ) such that ΓB is a connected (X, 2)-arctransitive graph and Γ is not a multicover of ΓB. A characterization of (Γ,X,B) was given in [20] for the case where |Γ(C) ∩ B| = 2 for B ∈ B and C ∈ ΓB(B). This motivates us to investigate the case where |Γ(C) ∩ B| = 3, that is, Γ[B,C] is isomorphic to one of 3K2, K3,3 − ...

Slovenija Abstract An innnite family of cubic edge-transitive but not vertex-transitive graph graphs with edge stabilizer isomorphic to Z Z 2 is constructed.

Let 0 be a simple graph and let G be a group of automorphisms of 0. The graph is (G, 2)-arc transitive if G is transitive on the set of the 2-arcs of 0. In this paper we construct a new family of (PSU(3, q2), 2)-arc transitive graphs 0 of valency 9 such that Aut0 = Z3.G, for some almost simple group G with socle PSU(3, q2). This gives a new infinite family of non-quasiprimitive almost simple gr...

A decomposition of a graph is a partition of the edge set. One can also look at partitions of the arc set but in this talk we restrict our attention to edges. If each part of the decomposition is a spanning subgraph then we call the decomposition a factorisation and the parts are called factors. Decompositions are especially interesting when the subgraphs induced by each part are pairwise isomo...

This paper concerns finite, edge-transitive direct and strong products, as well as infinite weak Cartesian products. We prove that the direct product of two connected, non-bipartite graphs is edge-transitive if and only if both factors are edgetransitive and at least one is arc-transitive, or one factor is edge-transitive and the other is a complete graph with loops at each vertex. Also, a stro...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...