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Algorithmic and explicit determination of the Lovász number for certain circulant graphs. (English) Zbl 1123.05085
Summary: We consider the problem of computing the Lovász theta function for circulant graphs \(C_{n,J}\) of degree four with \(n\) vertices and chord length \(J\), \(2 \leqslant J \leqslant n\). 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 \(J = 3\).

MSC:
05C85 Graph algorithms (graph-theoretic aspects)
94A40 Channel models (including quantum) in information and communication theory
Software:
SDPpack
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