Exept from the K_{n,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?

Conjecture:

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.

**Last update: February 25th, 2011**

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