Abstract
FAMILY OF CIRCULANT GRAPHS AND ITS EXPANDER PROPERTIES by Vinh Kha Nguyen In this thesis, we apply spectral graph theory to show the non-existence of an expander family within the class of circulant graphs. Using the adjacency matrix and its properties, we prove Cheeger’s inequalities and determine when the equalities hold. In order to apply Cheeger’s inequalities, we compute the spectrum of a general circulant graph and approximate its second largest eigenvalue. Finally, we show that circulant graphs do not contain an expander family.
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