Exact formulae for the Lovasz Theta Function of sparse Circulant Graphs

Abstract

The Lovasz theta function has attracted a lot of attention for its connection with diverse issues, such as communicating without errors and computing large cliques in graphs. Indeed this function enjoys the remarkable property of being computable in polynomial time, despite being sandwitched between clique and chromatic number, two well known hard to compute quantities. In this paper I provide a closed formula for the Lovasz function of a specific class of sparse circulant graphs thus generalizing Lovasz results on cycle graphs (circulant graphs of degree 2)