Exept from the Kn,n graphs there are known exactly seven triangle free strongly regular graphs at this moment. The open problem that remains is: Is there an eighth triangle free strongly regular graph?
There exists a 57-regular Moore graph
If this conjecture is true, an 8th triangle free strongly regular graph is found.
For understanding the problem, first read a few definitions.
Click here for the seven known triangle free strongly regular graphs.
The problem description comes from the Open Problem Garden. There are two versions: There exist a 57-regular graph with diameter 2 and girth 5 (this would be a Moore graph), and: There is an eighth triangle free strongly regular graph.
The original problem you can find at the following list:
Godsil, C. D., Problems in Algebraic Combinatorics, Electronic Journal of Combinatorics, Volume 2, F1.