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Digraphical Regular Representations of Infinite Finitely Generated Groups

✍ Scribed by R.G. Möller; N. Seifter

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
104 KB
Volume
19
Category
Article
ISSN
0195-6698

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✦ Synopsis

A directed Cayley graph X is called a digraphical regular representation (DRR) of a group G if the automorphism group of X acts regularly on X . Let S be a finite generating set of the infinite cyclic group Z. We show that a directed Cayley graph X (Z, S) is a DRR of Z if and only if

As a general result we prove that a Cayley graph X of a finitely generated torsion-free nilpotent group N is a DRR if and only if no non-trivial automorphism of N of finite order leaves the generating set invariant.

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