Geodesic
The beta-polynomials of Complete Graphs are Real
Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 1 .

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A polynomial is said to be real if all its zeros are real. It has been conjectured that the $\beta$-polynomials of all graphs are real. In this paper we show that the conjecture is true for complete graphs. In fact, we obtain a more general result, namely that certain linear combinations of Hermite polynomials are real.
Classification : 05C50 05C70 
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     title = {The beta-polynomials of {Complete} {Graphs} are {Real}},
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Xueliang Li; Ivan Gutman; Gradimir V. Milovanović. The beta-polynomials of Complete Graphs are Real. Publications de l'Institut Mathématique, _N_S_67 (2000) no. 81, p. 1 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_67_81_a0/