Abstract
Abstract In this paper we first study some properties of circulant graphs of degree four. In particular, we determine their clique and chromatic numbers and address issues related to their Lovasz theta function. We also consider generalizations of circulant graphs, called generalized circulants, that possess certain interesting properties, such as high connectivity and comparatively small clique number. Classes of generalized circulants may have an arbitrarily large gap between the clique and the chromatic number.
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