کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775242 | 1413578 | 2017 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Coulson-type integral formulas for the general Laplacian energy-like invariant of graphs II
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let G be a graph of order n and λ1â¥Î»2â¥â¯â¥Î»n be the eigenvalues of G. The energy of G is defined as E(G)=âk=1n|λk|. A well-known result regarding the energy of graphs is the Coulson integral formula, which defines the relationship between the energy and the characteristic polynomial of graphs. Let μ1â¥Î¼2â¥â¯â¥Î¼n=0 be the Laplacian eigenvalues of G. The general Laplacian energy-like invariant of G, denoted by LELα(G), is defined as âμkâ 0μkα when μ1â 0, and 0 when μ1=0, where α is a real number. In this study, we give some Coulson-type integral formulas for the general Laplacian energy-like invariant of graphs in the case where α is a rational number. Based on this result, we also give some Coulson-type integral formulas for the general energy and general Laplacian energy of graphs in the case where α is a rational number. We also show that our formulas hold when α is an irrational number where 0<|α|<1, whereas they do not hold when |α|>1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 2, 15 May 2017, Pages 1725-1740
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 2, 15 May 2017, Pages 1725-1740
نویسندگان
Lu Qiao, Shenggui Zhang, Jing Li,