Chromatic roots as algebraic integers by Adam Bohn

“…By computing the chromatic polynomials of two large families of graphs, we prove the $α +n$ conjecture for quadratic and cubic integers, and show that the set of chromatic roots satisfying the nα conjecture is dense in the complex plane.…”
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Integral Laplacian graphs with a unique repeated Laplacian eigenvalue, I by Hameed Abdul, Tyaglov Mikhail

“…We also show close relations between graphs realizing Si,n{S}_{i,n} and S{i,j}nm{S}_{{\left\{i,j\right\}}_{n}^{m}} and discuss the so-called Sn,n{S}_{n,n}-conjecture and the corresponding conjecture for S{i,n}nm{S}_{{\left\{i,n\right\}}_{n}^{m}}.…”
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