Abstract
Graphs with few distinct eigenvalues form an interesting class of
graphs. Clearly if all the eigenvalues of a graph coincide, then we
have a trivial graph (a graph without edges). Connected graphs with
only two distinct eigenvalues are proven to be complete graphs. The
first nontrivial graphs with three distinct eigenvalues are the
strongly regular graphs. Graphs with exactly three distinct
eigenvalues are generalizations of strongly regular graphs by
dropping regularity. A large family of (in general) nonregular
examples is given by the complete bipartite graphs $K_{m,n}$. Other
examples were found by Bridges, Mena, Muzychuk and Klin, most of
them being cones. Those with the least eigenvalue $2$ have been
characterized by Van Dam. In this talk we give some results on
graphs with few distinct eigenvalues. Moreover we consider graphs
with three distinct eigenvalues and we characterize those with the
largest eigenvalue less than 8.
Information:
Date:  Wednesday, August 27, 2008, 10:0011:00  Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
