کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775467 | 1631736 | 2018 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Coulson-type integral formulas for the general energy of polynomials with real roots
ترجمه فارسی عنوان
فرمول انتگرالی نوع کولسون برای انرژی کلی چندجملهای با ریشه های واقعی
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In 1940 Coulson obtained an important integral formula which makes it possible to calculate the energy of a graph without knowing its spectrum. Recently several Coulson-type integral formulas have been obtained for various energies and some other invariants of graphs based on eigenvalues. For a complex polynomial Ï(z)=âk=0nakznâk=a0âk=1n(zâzk) of degree n and a real number α, the general energy of Ï(z), denoted by Eα(Ï), is defined as âzkâ 0|zk|α when there exists k0â{1,2,â¦,n} such that zk0â 0, and 0 when z1=â¯=zn=0. In this paper we give Coulson-type integral formulas for the general energy of polynomials whose roots are all real numbers in the case that αâQ. As a consequence of this result, we obtain an integral formula for the 2l-th spectral moment of a graph. Furthermore, we show that our formulas hold when α is an irrational number with 0â¯<â¯|α|â¯<â¯2 and do not hold with |α|â¯>â¯2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 320, 1 March 2018, Pages 202-212
Journal: Applied Mathematics and Computation - Volume 320, 1 March 2018, Pages 202-212
نویسندگان
Lu Qiao, Shenggui Zhang, Jing Li,