What is known about the range of spectra of regular graphs? That is, I wish to know the largest intervals in which the minimum and maximum eigenvalues of a graph lie. For example, it is known that the largest eigenvalue of a graph lies in between the maximum and average degrees of the graph. For regular graphs, the maximum eigenvalue is just the maximum degree. Are there any bounds on the minimum eigenvalues.
I wish to also know whether there are better bounds for graphs like (regular) line graphs, bipartite graphs, total graphs etc. Thanks beforehand.
