Graph switching is a collective term for operations that produce a new graph from a given graph by changing its adjacencies according to a prescribed rule. It does not refer to a unique operation.
The unqualified term "switching" often denotes Seidel switching, which exchanges edges and nonedges between a chosen subset 
of the vertex
set 
and 
(Seidel 1974).
Godsil-McKay switching chooses a vertex subset 
that induces a regular graph
and for which every vertex outside 
has 0, 
, or 
neighbors in 
. For each vertex having 
neighbors in 
, its neighbors and nonneighbors in 
are interchanged. The resulting graph is cospectral
with the original graph (Abiad et al. 2019).
Degree-preserving edge switching, also called a 2-switch, replaces two vertex-disjoint edges by one of the other two pairings of their four endpoints, provided the replacement edges are not already present. This operation preserves the degree sequence and is the switching used in the definitions of switchable and unswitchable graphs (Mukhopadhyay et al. 2023).
