PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 67(81), pp. 16 (2000) 

The $\beta$polynomials of complete graphs are realXueliang Li, Ivan Gutman and Gradimir Milovanovi\'cDepartment of Applied Mathematics, Northwestern Polytechnical University, X'ian, Shaanxi 710072, China and Prirodnomatematicki fakultet, Kragujevac, Yugoslavia and Elektronski fakultet, Nis, YugoslaviaAbstract: 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 (MSC2000): 05C50; 05C70 Full text of the article:
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