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...

We show that the satisfiability problem for the two-variable first-order logic, FO2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO2l...

It has previously been shown that transitive verbs are more difficult to recall than intransitive. Experiment I replicated this finding. Experiment II examined the associations to, and response latencies of, transitive and intransitive verbs. Latencies of responses did not differ, but the form class of responses was significantly different. Transitive verbs elicited more noun responses. It is s...

A graph is called cubic and tetravalent if all of its vertices have valency 3 and 4, respectively. It is called vertex-transitive and arc-transitive if its automorphism group acts transitively on its vertex-set and on its arcset, respectively. In this paper, we combine some new theoretical results with computer calculations to construct all cubic vertex-transitive graphs of order at most 1280. ...

The complementary prism of a graph Γ is the ΓΓ̄, which formed from union and its complement Γ̄ by adding an edge between each pair identical vertices in Γ̄. Vertex-transitive self-complementary graphs provide vertex-transitive prisms. It was recently proved author that ΓΓ̄ core, i.e. all endomorphisms are automorphisms, whenever vertex-transitive, self-complementary, either core or complete graph. ...