We give a necessary and su cient condition for a graphical regu lar representation to be adjacency transitive and provide an in nite family of nite simple undirected vertex transitive graphs such that neither nor c is adjacency transitive

In this paper, we will determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this will complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we deter...

We consider the problem of classifying all finite basis-transitive matroids and reduce it to the classification of the finite basis-transitive and point-primitive simple matroids (or geometric lattices, or dimensional linear spaces). Our main result shows how a basisand point-transitive simple matroid is decomposed into a so-called supersum. In particular each block of imprimitivity bears the s...

In early 2000’s, Rivest [Riv00,MR02] and Micali [MR02] introduced the notion of transitive signature, which allows a third party to generate a valid signature for a composed edge (vi, vk), from the signatures for two edges (vi, vj) and (vj , vk), and using the public key only. Since then, a number of works, including [MR02,BN02,Hoh03,SFSM05,BN05], have been devoted on transitive signatures. Mos...

In this thesis we shall deal with oriented graphs. The motivation for us is a result by Sali and Simonyi (see also a short proof by Gyárfás) where the existence of the decomposition of transitive tournaments on two isomorphic graphs is shown. In this thesis we start to study a problem of packing in transitive tournaments and we consider decompositions and partitions of transitive tournaments. T...