Integral trees of odd diameters

A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvari proved the existence of integral trees of any even diameter. In the odd case, integral trees have been constructed with diameter at most 7. In this article, we show that for every odd integer n>1, there are infinitely many integral trees of diameter n. © 2011 Wiley Periodicals, Inc. J Graph Theory, © 2012 Wiley Periodicals, Inc. (Contract grant sponsor: IPM (to E. G. and A. M.).)