Is there a term in graph theory called 'GRAIL'?

Question

I've been a talk with a PhD student about some graph issue and told me about GRAIL graph and have drawn it for me as you see in the picture, however, I try to generalize so-called "Grail graph" to k-pair problem. But I am not able to find a definition, though.

In the picture is an example of 2-pair problem in the GRAIL graph.

http://postimg.org/image/4a3xvsik9/

so my question is: have you seen this kind of graph? or have you heard about this graph, or do you know a name for this graph (may be I misunderstood with this kind of graph).

I have to point that I found a paper called "GRAIL: Scalable Reachability Index for Large Graphs". However, it doesn't give me an example of a graph, instead it just give me a "a good scale for reachability graph between fixed two nodes";

Thank you.

Answer 1

Yes, there is a graph called GRAIL GRAPH.

I have found it first by trial-and-error searching technique among many papers of Network (branch of graph theory) and Information theory, a paper is published and written by C. Wang and N. B. Shroff. Moreover, I received a couple days ago an email from my friend telling me the reference for the name of the Grail graph and he sent me the same paper that I found.