A graph is said to be unswitchable if it cannot be reduced to another graph with the same degree sequence by edge-switching.
Conversely, a graph that can be reduced to another graph with the same degree sequence by edge-switching is known as a switchable graph.
Unswitchable graphs are characterized by forbidden induced subgraphs 
, 
, and 
, where 
is a cycle graph, 
a path graph, and 
is a ladder rung graph.
All unswitchable graphs are split graphs (Mukhopadhyay et al. 2023).
The numbers of unswitchable connected graphs on 
, 2, ... nodes are 1, 1, 2, 4, 8, 16, 32, 64, ..., (which
are powers of two), the first few of which are illustrated above. Similarly, the
numbers of simple not-necessarily-connected graphs are 1, 2, 4, 8, 16, 32, 64, 128,
....
