Let $G$ be a cirulant graph with no loops at vertices and vertex degree $d$. Is the Lovasz theta function of this graph given by: $\vartheta(G) = \max_{i}\frac{-N\epsilon_{i}}{-\epsilon_{i}+d-1}$?

where $\epsilon_{i}$ are the eigenvalues of the adjacency matrix $A$ of the graph and is given by $\epsilon_{i} = 2\sum_{j=2}^{\frac{N-1}{2}}a_{j}cos(\frac{2\pi(j-1)i}{N})$ where $a_{j}$ values a_{j} \in \{0,1\}$ form the first row of $A$.

Let $G$ be a cirulant graph with no loops at vertices and vertex degree $d$. Is the Lovasz theta function of this graph given by: $\vartheta(G) = \max_{i}\frac{-N\epsilon_{i}}{-\epsilon_{i}+d-1}$?

where $\epsilon_{i}$ are the eigenvalues of the adjacency matrix $A$ of the graph and is given by $\epsilon_{i} = 2\sum_{j=2}^{\frac{N-1}{2}}a_{j}cos(\frac{2\pi(j-1)i}{N})$ where $a_{j}$ values form the first row of $A$.