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On the number of integral graphs
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https://doi.org/10.1016/j.laa.2015.11.027Abstract
We show that at most a 2-cn3/2 proportion of graphs on n vertices have integral spectrum. This improves on previous results of Ahmadi, Alon, Blake, and Shparlinski (2009), who showed that the proportion of such graphs was exponentially small.
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