A regular graph is called semisymmetric if it is edge-transitive but not vertex-transitive. It is proved that the Gray graph is the only cubic semisymmetric graph of order 2p3, where p 3 is a prime.

A regular graph is called semisymmetric if it is edge transitive but not vertex transitive It is proved that the Gray graph is the only cubic semisymmetric graph of order p where p is a prime

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...

This paper introduces a family of tetravalent graphs called rose window graphs, denoted by Rn(a, r), and investigates their symmetry properties. Four families of these graphs are shown to be edge-transitive and it is conjectured that every Rn(a, r) which is edge-transitive belongs to one of these families. Proofs and conjectures about the size of a dart-stabilizer and about regular maps contain...

ion Rules Abst1: Variable instantiations with essential ground terms of complexity r (using a modified version of our work [SMT’2013]) Abst2: φ := (l ∨ φrest), (¬l ∨ Crest) ∈ CNF (F ) =⇒ φ φ[Crest / l ] Abst3: φ := (¬φ(t) ∨ φrest), t := pg =⇒ φ φ[(∀x . x = t ∨ (t, x)d ∈ tcR → φ(x)) / φ(t)]

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; transitive closure; and the...

It is shown that the graph QQ) C obtained from the 7 -cube QQ) by deletion of a perfect Hamming code C has a spanning self-complementary subgraph which is edge-transitive but not vertextransitive and also extremal among all the cube subgraphs which are square-blocking and codeavoiding. Our work uses combinatorial techniques involving orientations on the Fano plane and the resulting Steiner trip...