Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially...

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...

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 ...