As defined by DeAlba et al. (2009) and references on the American Institute of Mathematics Minimum Rank Graph Catalogs, an 
-pineapple graph is a graph obtained by adding 
pendant vertices to one of the vertices of the complete
graph 
,
where 
and 
.
Pineapple graphs for small 
are illustrated above.
The degenerate case of 
corresponds to an 
-lollipop graph. Other special cases are summarized
in the following table.
 | named graph |
 | paw graph |
 | cricket graph |
