Constructing symmetric drawings of graphs is NP-hard. In this paper, we present a new method for drawing graphs symmetrically based on group theory. More formally, we define an n-geometric automorphism group as a subgroup of the automorphism group of a graph that can be displayed as symmetries of a drawing of the graph in n dimensions. Then we present an algorithm to find all 2and 3-geometric a...

We exhibit an interesting Cayley graph X of the elementary abelian group Z6 2 with the property that Aut(X) contains two regular subgroups, exactly one of which is normal. This demonstrates the existence of two subsets of Z6 2 that yield isomorphic Cayley graphs, even though the two subsets are not equivalent under the automorphism group of Z6 2 . 2000 Mathematics subject classification: 05C25.

The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C. We also prove that, with the exception of hypersurfaces of the form v = |z|, local automorphisms are always determined by their 1-jets. Using this result, in the second part we describe special normal forms which by an additional normalization eliminate t...

This paper deals with the relation between the automorphism groups of some paving matroids and Z3, where Z3 is the additive group of modulo 3 over Z. It concludes that for paving matroids under most cases, Z3 is not isomorphic to the automorphism groups of these paving matroids. Even in the exceptional cases, we reasonably conjecture that Z3 is not isomorphic to the automorphism groups of the c...

Let X be a connected locally finite graph with vertex-transitive automorphism group. If X has polynomial growth then the set of all bounded automorphisms of finite order is a locally finite, periodic normal subgroup of AUT(X) and the action of AUT(X) on V(X) is imprimitive if X is not finite. If X has infinitely many ends, the group of bounded automorphisms itself is locally finite and periodic.

It is known that a number of algebraic properties of the braid groups extend to arbitrary finite Coxeter type Artin groups. Here we show how to extend the results to more general groups that we call Garside groups. Define a Gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths, and where left and right lower common multiples...

Let F = (Kn,P) be a circulant homogeneous factorisation of index k, that means P is a partition of the arc set of the complete digraph Kn into k circulant factor digraphs such that there exists σ ∈ Sn permuting the factor circulants transitively amongst themselves. Suppose further such an element σ normalises the cyclic regular automorphism group of these circulant factor digraphs, we say F is ...

Let Γ be a graph and let G be a group of automorphisms of Γ. The graph Γ is called G-normal if G is normal in the automorphism group of Γ. Let T be a finite non-abelian simple group and let G = T l with l ≥ 1. In this paper we prove that if every connected pentavalent symmetric T -vertex-transitive graph is T -normal, then every connected pentavalent symmetric G-vertex-transitive graph is G-nor...

Computational techniques are described for the automorphism groups of edge-weighted graphs. Fortran codes based on the manipulation of weighted adjacency matrices are used to compute the automorphism groups of several edge-weighted graphs. The code developed here took 37l/2 min of CPU time to generate 1 036 800 permutations in the automorphism group of an edge-weighted graph.