Ball and Coxeter (1987, pp. 277-278) define the ladder graph 
, here called the ladder rung graph, of order 
as the graph union of 
copies of the path
graph 
.
The 
-ladder
rung graph is isomorphic to the Haar graph 
and to the Knödel
graph 
.
Kneser graphs of the form 
are ladder rung graphs of order 
, where 
is a central
binomial coefficient.
The graph complement of 
is the cocktail party
graph 
.
If the restriction 
in the I graph 
is loosened, 
corresponds to 
.
Ladder rung graphs are trivially unit-distance graphs.
has chromatic
polynomial, independence polynomial,
and matching polynomial are given by
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
with corresponding recurrence equations
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
The bipartite double graph of 
is 
.
