The Language of Self-Avoiding Walks
Connective Constants of Quasi-Transitive Graphs| By: | Christian Lindorfer |
| Publisher: | Springer Nature |
| Print ISBN: | 9783658247638 |
| eText ISBN: | 9783658247645 |
| Edition: | 0 |
| Copyright: | 2018 |
| Format: | Page Fidelity |
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The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a formal grammar, which can be used to calculate the connective constant of the graph. Christian Lindorfer discusses the methods in some examples, including the infinite ladder-graph and the sandwich of two regular infinite trees.