PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 67(81), pp. 1--6 (2000)
The $\beta$-polynomials of complete graphs are real
Xueliang Li, Ivan Gutman and Gradimir Milovanovi\'cDepartment of Applied Mathematics, Northwestern Polytechnical University, X'ian, Shaanxi 710072, China and Prirodno-matematicki fakultet, Kragujevac, Yugoslavia and Elektronski fakultet, Nis, Yugoslavia
Abstract: 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
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