Behruz Tayfeh-Rezaie: Integral graphs and trees
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Abstract: A graph is called integral if all eigenvalues of its 
adjacency matrix consist entirely of integers. Integral graphs 
are very rare and difficult to find. We first introduce some general
methods for constructing such graphs. As a consequence, some infinite 
families of integral graphs are obtained. We then pay our attention 
to trees where we discuss the recent  construction of  integral trees 
with arbitrary large diameter. Finally, we  prove that for a given 
nullity more than 1, there are only finitely many integral trees.