A graph Γ admitting a group H of automorphisms acting semi-regularly on the vertices with
exactly two orbits is called a bi-Cayley graph over H. This generalisation of a Cayley graph …

A k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give
a basic theory of k-orbit maps and classify them up to k⩽ 4.“Hurwitz-like” upper bounds for …

This is the first in the series of articles stemming from a systematical investigation of finite
edge-transitive tetravalent graphs, undertaken recently by the authors. In this article, we …

Abstract polytopes are combinatorial structures that generalize the classical notion of convex
polytopes. In this paper particular attention is given to polytopes whose automorphism …

We extend the notion of symmetry type graphs of maps to include maniplexes and (abstract)
polytopes, using them to study k-orbit maniplexes (where the automorphism group has k …

The paper gives a collection of open problems on abstract polytopes that were either
presented at the Polytopes Day in Calgary or motivated by discussions at the preceding …

We determine all factorisations X= AB, where X is a finite almost simple group and A, B are
core-free subgroups such that A∩ B is cyclic or dihedral. As a main application, we classify …

For every polytope there is the universal regular polytope of the same rank as-automorphism
of a given order. As an application, we analyze properties of self-dual edge-transitive …

Symmetries of Equivelar 4-Toroids | Discrete & Computational Geometry Skip to main
content SpringerLink Account Menu Find a journal Publish with us Search Cart 1.Home 2.Discrete …

Recipes for edge-transitive tetravalent graphs* Page 1 ISSN 2590-9770 The Art of Discrete
and Applied Mathematics 3 (2020) #P1.08 https://doi.org/10.26493/2590-9770.1269.732 (Also …