Algorithmic and explicit determination of the Lovasz number for certain circulant graphs

We consider the problem of computing the Lovasz theta function for circulant graphs C-n,C-J of degree four with n vertices and chord length J, 2 <= J <= n. We present an algorithm that takes O(J) operations if J is an odd number, and O(n/J) operations if J is even. On the considered class of graphs our algorithm strongly outperforms the known algorithms for theta function computation. We also provide explicit formulas for the important special cases J = 2 and J = 3. Published by Elsevier B.V.