Connectivity of Addition Cayley Graphs

TL;DR

This paper characterizes the connectivity of addition Cayley graphs on finite abelian groups and describes their minimum vertex cuts when not complete.

Contribution

It provides a complete determination of connectivity and explicit descriptions of minimum vertex cuts for addition Cayley graphs on finite abelian groups.

Findings

Connectivity is explicitly determined for all such graphs.

Non-complete graphs have a minimum vertex cut of a specific form.

The results apply to all finite abelian groups.

Abstract

For any finite abelian group $G$ and any subset $S\seq G$, we determine the connectivity of the addition Cayley graph induced by $S$ on $G$. Moreover, we show that if this graph is not complete, then it possesses a minimum vertex cut of a special, explicitly described form.