In this paper, we characterise the family of finite arc-transitive bicirculants. We show that every bicirculant is a normal r $r$ -cover an graph lies in one eight infinite families or seven sporadic graphs. Moreover, each these ‘basic’ graphs either circulant, and latter case has for some integer .

Transitive Inference is a form of deductive reasoning that has been suggested as one cognitive mechanism by which animals could learn the many relationships within their group's dominance hierarchy. This process thus bears relevance to the social intelligence hypothesis which posits evolutionary links between various forms of social and nonsocial cognition. Recent evidence corroborates the link...

In this paper, we study a time-periodic model, which incorporates seasonality and host stage-structure. This model describes the propagation of Puumala hantavirus within bank vole population Clethrionomys glareolus. The basic reproduction number R0 is obtained. By appealing to theory monotone dynamical systems chain transitive sets, establish threshold-type result on global dynamics in terms R0...

Finite graphs of valency 4 and girth 4 admitting 1 2-transitive group actions, that is vertex-and edge-but not arc-transitive group actions, are investigated. A graph is said to be 1 2-transitive if its automorphism group acts 1 2-transitively. There is a natural (balanced) orientation of the edge set of a 1 2-transitive graph induced and preserved by its auto-morphism group. Among others it is...

A code in a graph 0 is a non-empty subset C of the vertex set V of 0. Given C , the partition of V according to the distance of the vertices away from C is called the distance partition of C . A completely regular code is a code whose distance partition has a certain regularity property. A special class of completely regular codes are the completely transitive codes. These are completely regula...

1 Multiply transitive groups Theorem 1.1. Let Ω be a finite set and G ≤ Sym(Ω) be 2–transitive. Let N E G be a minimal normal subgroup. Then one of the following holds: (a) N is regular and elementary abelian. (b) N is primitive, simple and not abelian. Proof. First we show that N is unique. Suppose that M is another minimal normal subgroup of G, so N ∩M = {e} and therefore [N,M ] = {e}. Since ...

A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let p be a prime. Cheng and Oxley [On weakly symmetric graphs of order twice a prime, J. Combin. Theory B 42(1987) 196-211] proved that there is no half-arc-transitive graph of order 2p, and Alspach and Xu [ 12 -transitive graphs of order 3p, J. Algebraic Combin. 3(1994) 347-355] c...

We explore the relation between vertexand edge-transitivity and arc-transitivity of various graphs. We exhibit several families of graphs whose vertexand edgetransitivity imply arctransitivity. In particular, we show that any vertexand edgetransitive graph with twice a prime number of vertices is arctransitive by simplifying the proof of a theorem by Cheng and Oxley, in which they classify all ...

Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ , where ρ is (m,n)semiregular for some integers m ≥ 1, n ≥ 2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ has at least one fixed vertex. A halfarc-transitive graph is a vertexand edgebut not arc-transitive graph. In this arti...