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Integral trees of odd diameters

By E. Ghorbani, A. Mohammadian and B. Tayfeh-rezaie


A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvári 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 paper, we show that for every odd integer n> 1, there are infinitely many integral trees of diameter n

Topics: Integral tree, Adjacency eigenvalue, Diameter
Year: 2011
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