The post is related to:https://mathoverflow.net/questions/59631/lovasz-theta-function-and-independence-number-of-product-of-simple-odd-cyclesHow far away is the Lovasz bound from the zero-error capacity of regular graphs? Are there any examples where the Lovasz bound is known to be not equal to the zero-error capacity of a regular graph? (This was answered below by Oleksandr Bondarenko.)In particular is any strict inequality known for odd cycles of sides greater than or equal to $7$?UpdateWhat improvement is needed in spectral theory to improve the Lovasz theta function so that the gap between Shannon capacity and Lovasz Theta for the cases for which a gap exists could be lowered? (Note I am concerned only from spectral perspective)
Lovasz theta function and regular graphs (odd cycles in particular) - connections to spectral theory
graph theory;it.information theory