SavedAdd your journal

Journals / Fırat Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2004 / Cilt: 16 - Sayı: 2

Finding the largest eigenvalue of a Hermit operator and graph

Bir Hermit işleri ve çizitinin en alt özdeğerinin bulunması

Elif Tekin TARIM
Oktay SİNANOĞLU
Pages
319–326
Publication Date
2022-11-05
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Thus the least eigenvalue can be obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:All graphs which obtained in terms of each other by using Valency Interaction Formulas (VIFs) belong to the same equivalence classes [1-7].
📊
Key Findings & Data:Also, these graphs are represented by Hermitian operators [1-7].
💡
Conclusion & Impact:Thus the least eigenvalue can be obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

All graphs which obtained in terms of each other by using Valency Interaction Formulas (VIFs) belong to the same equivalence classes [1-7]. Also, these graphs are represented by Hermitian operators [1-7]. By using "simple pictorial rules" spectral spread is obtained with the eigenvalues of these graphs [8]. In this paper, our object is to find spectral radious namely the largest eigenvalue $lambda_1geqlambda_2geq...geqlambda_n$ by using "simple pictorial rules". Thus the least eigenvalue can be obtained.

Özet

Yapısal Eşdeğişim İlkesi'nin (VIF) kurallarıyla birbirinden elde edilen bütün çizitler aynı eşdeşlik sınıflarına aittirler[l-7]. Ayrıca bu çizitler Hermit işlerleriyle ("operatör") temsil edilir [1-7]. Basit resimli kural ile çizitlerin özdeğerleri bulunarak izgesel aralık elde edilir [8]. Çalışmamızda amaçlanan, izgesel yarıçapını ("spectral radious") yani en alt özdeğerini $lambda_1geqlambda_2geq...geqlambda_n$ şeklinde sıralanmış özdeğerlerden $lambda_1$'i) hesaplayan basit resimli formülü bulmaktır. Böylece en üst (en küçük) özdeğere de ulaşılabilir.

🔖

Cite This Article

TARIM, E. T., SİNANOĞLU, O. (2022). Finding the largest eigenvalue of a Hermit operator and graph. Fırat Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 16 - Sayı: 2, 319–326. https://ajindex.com/articles/650518

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. O. Sinanoğlu, Structural Covariance Of Graphs, Theoretica Chimica Acta (Berl.), 65, 255-265, 1984
  2. O. Sinanoğlu, A Principle Of Linear Covariance For Quantum Mechanics And The Electronic Structure Theory Of Molecules And Other Atom Clusters, Theoretica Chimica Acta (Berl.), 65, 233-242, 1984
  3. O. Sinanoğlu, Deformational Covariance Of Graphs, Theoretica Chimica Acta (Berl.), 65, 267-270
  4. O. Sinanoğlu, Non-Unitary Classification Of Molecular Electronic Structures And Other Atom Clusters, Theoretica Chimica Acta (Berl.), 65, 249-254, 1984
  5. O. Sinanoğlu, A Theorem For Qualitative Deductions In Organic Or Inorganic Chemistry Regarding The Realitive Stabilities, Distortions And Reactions Of Molecules, Chemical Pyhics Letters, 103, 4, 315-322, 1984
  6. O. Sinanoğlu, New Method For Qualitative Quantum Chemical Deductions On Organic Or Inorganic Molecules Or Clusters Directly from Structural Formulas Or ORTEP Diagrams, Theoretica Chimica Acta, 68, 251-270, 1985
  7. O. Sinanoğlu, “Sonlu Yöney Uzayları Üzerine Kurulan Cebirsel Yapılar, Hermit İşlerleri Ve Onları Temsil Eden Çizitlerin Cebirsel, Topolojik Sınıflara Ayrılması, Sınıf Değişmezleri; Yeni Eşdeğişim İlkesi; Nicem Fizik ve Kimyasına Uygulamalar”, F.Ü. Fen ve Müh. Bilimleri Dergisi, 11, 3, 329-344, 1999
  8. E.T. Tarım ve O. Sinanoğlu, Bir Hermit İşleri Ve Çizitinin En Alt Ve En Üst Özdeğerleri Arasındaki İzgesel Aralığın Bulunması, F.Ü. Fen ve Müh. Bilimleri Dergisi (baskıda), 2004
  9. D. Cvetkovic ve P. Rowlinson, The Largest Eigenvalue Of A Graph: A Survey, Linear Algebra and Its Applications, 28, 3-33, 1990
  10. O. Rojo ve R. Jiménez, A Decreasing Sequence of Upper Bounds for Perron Root, Computers Math. Applic., 28, 8, 9-15, 1994
  11. H.Yuan, A Bound On The Spectral Radius Of Graphs, Linear Algebra Appl., 108, 135-139, 1988
  12. H.S. Wilf, The Eigenvalues Of A Graph and Its Chromatic Numbers, J.London Mathematics Society, 42, 330-332, 1967
  13. R. Stanley, A Bound On The Spectral Radius Of Graphs With Edges, Linear Algebra and Its Applications, 87, 267-269, 1987
  14. O. Sinanoğlu, The New Pictorial Structural Covariance Method For Qualitative Quantum Chemistry II: Arenes With Or Without Polyene Side Chains and Polyene Bridges, Journal of Mathematical Chemistry, 2, 117-136, 1988
  15. O. Sinanoğlu, The New Pictorial Structural Covariance Method For Qualitative Quantum Chemistry III: Fused Polycyclics And Their Ions, Journal of Mathematical Chemistry, 2, 137-154, 1988
  16. O. Sinanoğlu, Chemic