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Dergiler / TWMS Journal of Applied and Engineering Mathematics / 2019 / Cilt: 9 - Sayı: 3

ON THE SPECTRA OF CYCLES AND PATHS

F. ÇELİK
I. N. CANGÜL
Sayfa
571–580
Yayın Tarihi
2019-09-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In particular, we prove that one can obtain the spectra of C2n and P2n+1 without detailed calculations just in terms of the spectra of Cn and Pn, respectively.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Energy of a graph was dened by E.
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Temel Bulgular & Veri:Huckel as the sum of absolute values of the eigenvalues of the adjacency matrix during the search for a method to obtain approximate solutions of Schrodinger equation which include the energy of the corresponding system for a class of molecules.
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Sonuç & Katkı:In particular, we prove that one can obtain the spectra of C2n and P2n+1 without detailed calculations just in terms of the spectra of Cn and Pn, respectively.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Spectrum of a graph · graph energy · recurrence relation

Abstract

Energy of a graph was dened by E. Huckel as the sum of absolute values of the eigenvalues of the adjacency matrix during the search for a method to obtain approximate solutions of Schrodinger equation which include the energy of the corresponding system for a class of molecules. The set of eigenvalues is called the spectrum of the graph and the spectral graph theory dealing with spectrums is one of the most interesting subareas of graph theory. There are a lot of results on the energy of many graph types. Two classes, cycles and paths, show serious dierences from others as the eigenvalues are trigonometric algebraic numbers. Here, we obtain the polynomials and recurrence relations for the spectral polynomials of these two graph classes. In particular, we prove that one can obtain the spectra of C2n and P2n+1 without detailed calculations just in terms of the spectra of Cn and Pn, respectively.

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Bu Makaleye Atıf Yap

ÇELİK, F., CANGÜL, I. N. (2019). ON THE SPECTRA OF CYCLES AND PATHS. TWMS Journal of Applied and Engineering Mathematics, Cilt: 9 - Sayı: 3, 571–580. https://ajindex.com/articles/846310

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