Is anything known about Lovasz Theta Function taking integral value in non-perfect graphs? In particular, does integral value of Lovasz theta always coincide with the size of largest independent set?

For instance, graph below is non-perfect, and its Lovasz theta function gives the independence number.

<img src="http://yaroslavvb.com/upload/save/non-perfect.png">

Its true for a few other non-perfect graphs I tried, here's a <a href="http://mathematica-bits.blogspot.com/2011/03/computing-lovasz-theta-function.html">Mathematica package </a> I used to compute it