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...

This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every subgroup G automorphism group a nontrivial design primitive affine or almost simple type. Moreover, we classify designs admitting flag transitive with socle PSL(n,q) for some n≥3. Alongside this analysis give construction 2-(v,k−1,k−2) given 2-(...

Among the properties of homogeneity of incidence structures flagtransitivity obviously is a particularly important and natural one. Consequently, in the last decades flag-transitive Steiner t-designs (i.e. flag-transitive t-(v, k, 1) designs) have been investigated, whereas only by the use of the classification of the finite simple groups has it been possible in recent years to essentially char...

In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ◦H is non-trivial and complete, then G ◦H is edge-transitive if and only if H is the lexicogr...