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

Abstract

We consider the problem of computing the Lovász theta function for circulant graphs Cn,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.

DOI: 10.1016/j.dam.2007.03.015

Cite this paper

@article{Brimkov2007AlgorithmicAE, title={Algorithmic and explicit determination of the Lov{\'a}sz number for certain circulant graphs}, author={Valentin E. Brimkov}, journal={Discrete Applied Mathematics}, year={2007}, volume={155}, pages={1812-1825} }