A non-complete graph Γ is said to be (G, 2)-distance-transitive if, for i = 1, 2 and for any two vertex pairs (u1, v1) and (u2, v2) with dΓ(u1, v1) = dΓ(u2, v2) = i, there exists g ∈ G such that (u1, v1) = (u2, v2). This paper classifies the family of (G, 2)-distancetransitive graphs of valency 6 which are not (G, 2)-arc-transitive.

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip3 or the complete graph K4, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of...

We define an on-line (incremental) algorithm that, given a (possibly infinite) pseudo-transitive oriented graph, produces transitive reorientation. This implies that theorem of Ghouila-Houri is provable in RCA 0 and hence computably true.

i.e. limT→+∞ π(T ) ehT /hT = 1. This generalized a result of Margulis for geodesic flows over manifolds of negative sectional curvature [6]. It is an interesting problem to estimate the error terms in such asymptotic formulae. In the particular case of geodesic flows over compact negatively curved manifolds we showed that there was an exponential error term (with a suitable principal term) [10]...

Symmetric graph designs, or SGDs, were deened by Gronau et al. as a common generalisation of symmetric BIBDs and orthogonal double covers. This note gives a classiication of SGDs admitting a 2-transitive automorphism group. There are too many for a complete determination, but in some special cases the determination can be completed, such as those which admit a 3-transitive group, and those with...

Given a connected graph and a vertex x ∈ V (G), the geodesic graph Px(G) has the same vertex set as G with edges uv iff either v is on an x − u geodesic path or u is on an x − v geodesic path. A characterization is given of those graphs all of whose geodesic graphs are complete bipartite. It is also shown that the geodetic number of the Cartesian product of Km,n with itself, where m,n ≥ 4, is e...

All node certificate based transitive signature schemes available in the literature make use of any digital signature scheme which is assumed to be provably secure against adaptive chosen-message attack, as a building block to produce node certificates in a graph. Consequently the algebraic structures to represent nodes in the graph are independent of the algebraic structure of signature scheme...

A version of generalised term graph rewriting is presented in which redirections are interpreted transitively. It is shown that the new semantics enjoy enhanced properties regarding ease of implementation on distributed machines compared with conventional semantics because of the Church-Rosser properties of transitive redirections. Furthermore, the good properties of orthogonal systems are larg...

For any g > 2 we construct a graph Γg ⊂ S whose exteriorMg = S\N(Γg) supports a complete finite-volume hyperbolic structure with one toric cusp and a connected geodesic boundary of genus g. We compute the canonical decomposition and the isometry group of Mg, showing in particular that any selfhomeomorphism of Mg extends to a self-homeomorphism of the pair (S ,Γg), and that Γg is chiral. Buildin...