The Pell graph 
is the graph defined as follows. Consider 
-tuples over 
such that maximal blocks of an odd
number of 2's are forbidden. Take these as the vertices
of the graph, and connect vertices
with an edge whenever they are equivalent except for
the exchange of a single 0 and 1 or a single 11 and 22.
The resulting graph 
has vertex count and edge count given by
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is a Pell
number (using the convention that 
, 
;
note that Munarini 2019 uses the alternate shifted convention 
, 
)
and
 |  |  |
(3)
|
 |  |  |
(4)
|
is the numerator of the 
th convergent of 
with 
a Chebyshev
polynomial of the first kind.
Special cases are summarized in the following table.
 | graph |
| 0 | singleton graph  |
| 1 | path graph  |
| 2 | banner graph |
The Pell graphs are bipartite (Munarini 2019) and median graphs (Munarini 2019, Došlić
and Podrug 2023). Since the Pell graph 
is an isometric subgraph of
the hypercube graph 
for 
(Munarini 2019), it is also a unit-distance
graph. It is also a subgraph of a Fibonacci
cube graph (Munarini 2019).
The Pell graphs 
,
, and 
are planar, while 
has graph
crossing number 12.
