One version of the polycirculant conjecture states that every vertex-transitive graph has a non-identity semiregular automorphism that is, a non-identity automorphism whose cycles all have the same length. We give a proof of the conjecture in the arc-transitive case for graphs of valency 8, which was the smallest open valency.

Let Γ be a graph and let G be a group of automorphisms of Γ. The graph Γ is called G-normal if G is normal in the automorphism group of Γ. Let T be a finite non-abelian simple group and let G = T l with l ≥ 1. In this paper we prove that if every connected pentavalent symmetric T -vertex-transitive graph is T -normal, then every connected pentavalent symmetric G-vertex-transitive graph is G-nor...

The automorphism groups of the symmetric 2-(64, 28, 12) designs with the symmetric difference property (SDP), as well as the groups of their derived and residual designs, are computed. The symmetric SDP designs all have transitive automorphism groups. In addition, they all admit transitive regular subgroups, or equivalently, (64, 28, 12) difference sets. These results are used for the enumerati...

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...

This paper forms part of a study of 2-arc transitivity for finite imprimitive symmetric graphs, namely for graphs admitting an automorphism groupG that is transitive on ordered pairs of adjacent vertices, and leaves invariant a nontrivial vertex partition B. Such a group G is also transitive on the ordered pairs of adjacent vertices of the quotient graph B corresponding toB. If in additionG is ...

This paper presents a method for constructing symmetric and transitive algorithms for registration of image sequences from image registration algorithms that do not have these two properties. The method is applicable to both rigid and nonrigid registration and it can be used with linear or periodic image sequences. The symmetry and transitivity properties are satisfied exactly (up to the machin...

on achieving my goal. His observations and comments helped me to establish the overall direction of the research and to move forward with investigation in depth. I would also like to thank my parents who gave me the opportunity to study. Without their support, I would have never got this far. Finally, I would like to dedicate this thesis to my wife, Yi-Chun, for her love, patience, and understa...

Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous archimedean t-norm are given. The first one aggregates the transitive closure R of R with a (maximal) T -transitive relation B contained in R. The second one modifies the values of R or B to better fit them with the ones of R.

The representation theorem Cor F-transitive fuzzy relations is used to prove that the set of reflexive, symmetric and F -transitive fuzzy relations on a set X, F being an Archimedean t-norm, is dense in the set of Ztransitive relations on X. It is also shown that any similarity relation can be represented as a limit of a sequence of transitive relations with respect to Archimedean t-norms.