Integral trees of odd diameters

E. Ghorbani; A. Mohammadian; B. Tayfeh-Rezaie

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arXiv · 1011.4666

Integral trees of odd diameters

E. Ghorbani·A. Mohammadian·B. Tayfeh-Rezaie

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Abstract

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 paper, we show that for every odd integer n > 1, there are infinitely many integral trees of diameter n.

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E. Ghorbani, A. Mohammadian, B. Tayfeh-Rezaie. 2010-11-21. Integral trees of odd diameters. https://arxiv.org/abs/1011.4666

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