The Cayley Graph of Neumann Subgroups

TL;DR

This paper characterizes all Cayley representations of the distant graph over integers as Neumann subgroups of the extended modular group, revealing their possible structures and realizability.

Contribution

It provides a complete classification of Cayley representations of the distant graph as Neumann subgroups and demonstrates their realizability.

Findings

All Cayley representations correspond to Neumann subgroups.

Possible structures of Neumann subgroups are identified.

Every structure can be realized.

Abstract

All Cayley representations of the distant graph $\Gamma _Z$ over integers are characterized as Neumann subgroups of the extended modular group. Possible structures of Neumann subgroups are revealed and it is shown that every such a structure can be realized.