The 
-book graph is defined as the graph
Cartesian product 
,
where 
is a star
graph and 
is the path graph on two nodes. The generalization
of the book graph to 
"stacked" pages is the 
-stacked book graph.
Special cases of the 
-book
graph are summarized below.
 | graph |
| 1 | square graph |
| 2 | domino graph |
Precomputed properties of book graphs are implemented in the Wolfram Language as GraphData[
"Book", m
].
The book graph 
is the simplex graph of the star
graph 
.
Book graphs of the form 
do not satisfy the parity condition for gracefulness and hence are ungraceful
(Gallian 2018). Maheo (1980) proved that 
is graceful and conjectured
that 
is graceful for all positive
integer 
.
Delorme (1980) provided a simpler graceful labeling for 
together with a graceful labeling for 
, thus establishing the conjecture.
The book graph 
has chromatic polynomial, independence
polynomial, matching polynomial, and rank polynomial given by
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  | ![(x-1)^(n-2)(x+1)^(n-2)[n^2x^2+(x^2-1)^3+n(-1+2x^2-2x^4)]](/images/equations/BookGraph/Inline28.svg) |
(3)
|
 |  | ![([1+3x(x+1)]^n(y-x)+x(y+1){1+x[3+x(3+y)]}^n)/y.](/images/equations/BookGraph/Inline31.svg) |
(4)
|
The corresponding recurrence relations are
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
 |  |  |
(8)
|
