Integral trees of odd diameters

Details Integral trees of odd diameters Integral trees of odd diameters

2010-11-21

arxiv.org/abs/1011.4666v1

Mathematics

Combinatorics

7 pages

Scientific paper

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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