Cayley graph of a group
From Groupprops
Definition
Let be a group and
be a generating set for
. The Cayley graph of
with respect to
is defined as follows:
- The vertex set of the graph is
.
- Given two distinct vertices
, there is an edge joining
to
if and only if
is in
.
We typically consider the Cayley graph for a finitely generated group and a finite generating set of the group. Further, we can assume without loss of generality that is a symmetric subset of
-- the inverse of any element of
is also in
.