The Pell graph 
is the graph defined as follows. Consider 
-tuples of 
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 
for 
(Munarini 2019), it is also a unit-distance
graph. It is also a subgraph of a Fibonacci cube
(Munarini 2019).
