A block graph, also called a clique tree, is a simple graph in which every block is a complete graph. The numbers of connected block
graphs on 
,
2, ... vertices are 1, 1, 2, 4, 9, 22, 59, 165, 496, ... (OEIS A035053).
Block graphs are chordal, distance-hereditary, geodetic, perfect, and Ptolemaic.
Classes of graphs which are block graphs include windmall graphs and trees.
A graph is a block graph if the lagest two of the distances
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
are equal.
