Some Graphs With Small Second Eigenvalue

Abstract:

In this article we discuss several very simple graphs which have fairly small eigenvalues. Perhaps the most important result is that one of the graphs is a Cayley graph whose corresponding Cayley hypergraphs have a second eigenvalue which is essentially as small as a Cayley hypergraph can have. Also, these
graphs are very simple to write down, and the eigenvalue calculation is based on the trace method and well known results about exponential sums.