The automorphism-group of an infinite graph acts in a natural way on the set of d-fibers (components of the set of rays with respect to the Hausdorff metric). For connected, locally finite, almost transitive graphs the kernel of this action is proved to be the group of bounded automorphisms. This co
A note on bounded automorphisms of infinite graphs
โ Scribed by Chris D. Godsil; Wilfried Imrich; Norbert Seifter; Mark E. Watkins; Wolfgang Woess
- Publisher
- Springer Japan
- Year
- 1989
- Tongue
- English
- Weight
- 439 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In [4] Jung and Watkins proved that for a connected infinite graph X either rยฎ(X) = oo holds or X is a strip, if Aut(X) contains a transitive abelian subgroup G. Here we prove the same result under weaker assumptions.
We present a construction of two infinite graphs \(G_{1}, G_{2}\) and of an infinite set of graphs such that \(\mathscr{F}\) is an antichain with respect to the minor relation and, for every graph \(G\) in \(\mathscr{F}\), both \(G_{1}\) and \(G_{2}\) are subgraphs of \(G\) but no graph obtained fro
Given an infinite graph G, let deg,(G) be defined as the smallest d for which V(G) can be partitioned into finite subsets of (uniformly) bounded size such that each part is adjacent to at most d others. A countable graph G is constructed with de&(G) > 2 and with the property that [{y~V(G):d(x, y)sn}