Some Graphs With Small Second Eigenvalue
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.