Vinsamlegast notið þetta auðkenni þegar þið vitnið til verksins eða tengið í það: http://hdl.handle.net/1946/26222
This thesis is a study of infinite directed graphs, and how we can use tools from the theory of group actions to investigate them. For a group \(G\) acting on a set \(\Omega\), we define a group homomorphism from \(G\) to the multiplicative group of positive rational numbers, using the suborbits of the group action. This homomorphism will be called the suborbit function and we will see that it is equal to a well known function, defined on locally compact topological groups, called the modular function.
There are a few objectives, and all main results are proved using the suborbit function.
The first objective is to generalize a result of Cheryl E. Praeger from 1991 about homomorphic images of infinite directed graphs with certain additional properties.
The second objective is to find a condition on edge transitive digraphs making them highly arc transitive.
Next, we define Cayley-Abels digraphs of groups and use the suborbit function to give a lower bound on their valency. Then we consider the growth of graphs, showing that all infinite digraphs with the same additional properties as in Praeger's result, have exponential growth.
Finally, the last chapter is dedicated to constructing examples using Cartesian products of digraphs.
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GroupActionsonInfiniteGraphs.pdf | 1.47 MB | Opinn | Heildartexti | Skoða/Opna | |
Skemman_yfirlysing_16.pdf | 374.85 kB | Lokaður | Yfirlýsing |