Teichmüllerraum für total degenerierte Kurven.
Testing Cayley graph densities
We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an -generated group is amenable if and only if the density of the corresponding Cayley graph equals to . We test amenable and non-amenable...
Tetravalent Arc-Transitive Graphs of Order 3p 2
Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p2 is given
Tetravalent half-arc-transitive graphs of order
We classify tetravalent -half-arc-transitive graphs of order , where and , are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.
Tetravalent non-normal Cayley graphs of order .
The accessibility of finitely presented groups.
The Action of Nilpotent Groups on Infinite Graphs.
The Cayley graph and the growth of Steiner loops
We study properties of Steiner loops which are of fundamental importance to develop a combinatorial theory of loops along the lines given by Combinatorial Group Theory. In a summary we describe our findings.
The Cayley graphs of and the limits of vertex-primitive graphs of -type.
The classification of finite groups by using iteration digraphs
A digraph is associated with a finite group by utilizing the power map defined by for all , where is a fixed natural number. It is denoted by . In this paper, the generalized quaternion and -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a -group are determined for a -group to be a generalized quaternion group. Further, the classification of two generated -groups as abelian or non-abelian...
The Decomposition of a General Graph according to a Given Abelian Group
The diameter of the character degree graph..
The distinguishing chromatic number.
The Farey graph.
The genera, reflexibility and simplicity of regular maps
This paper uses combinatorial group theory to help answer some long-standing questions about the genera of orientable surfaces that carry particular kinds of regular maps. By classifying all orientably-regular maps whose automorphism group has order coprime to , where is the genus, all orientably-regular maps of genus for prime are determined. As a consequence, it is shown that orientable surfaces of infinitely many genera carry no regular map that is chiral (irreflexible), and that orientable...
The graph of generating sets of an abelian group
The group of autotopies of a digraph
The influence of symmetry on the probability of assembly pathways for icosahedral viral shells.
The Mathieu group and its pseudogroup extension .
The maximum order of finite groups of outer automorphisms of free groups.