What is the Algorithm to find all the possible chordal graphs which can be formed by a given 'n' number of vertices A chordal Graph is a connected graph which contains no chord-less cycle of size greater than three.
They are also called as Triangulated graphs. 

All Paths are Chordal Graphs (No cycles).

All Trees are chordal Graphs (No cycles).

All cliques are chordal graphs. 

A Path contains the minimum no of edges and a clique contains the maximum number of edges of a given n vertices chordal graph

Wiki Link for more explanation of chordal graphs  

So for a fixed number 'n', what is the algorithm to find all the possible chordal graphs of n vertices? 

For example: 


n= 2, Answer = 1 chordal graph. 
n= 3, Answer = 2 chordal graphs, 
n= 4, Answer = 5 chordal graphs, 
n= 5, Answer = 15 chordal graphs.


The above are determined by drawing all possible examples. Any algorithm?
The best way to do it, if you want to generate billions of graphs is to read up on enumeration algorithms such as:

[Yasuko Matsui, Ryuhei Uehara and Takeaki Uno, Enumeration of Perfect Sequences of Chordal Graph (2008)]

However for many this may be more than what is needed.
An easier algorithm is:


Enumerate all chordal graphs on n-1 vertices.
For each chordal graph G on n-1 vertices and each clique C in G.
Create a graph G' by adding a vertex v with neighbours C.
If G' has not already been found, add G to the list of chordal graphs on n vertices.


By this algorithm you should be able to generate the chordal graphs on at most 11 vertices which means over a million graphs.