Lovasz theta of even cycle
The Lovász theta function is bounded between the independence number and the clique covering number (the chromatic number of the complementary graph). For even cycles, both numbers are $n/2$. For example, for the $6$-cycle with vertices $1,2,3,4,5,6$, there are independent sets of size $3$, e.g. $\{1,3,5\}$, and the graph can be covered with the $3$ cliques $\{1,2\},\{3,4\},\{5,6\}$.