№ 59-4 (том 1): ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, Февраль, 2025
Научно-образовательные статьи

EIGENVALUES OF REGULAR GRAPHS: KEY PROPERTIES, EXAMPLES, AND APPLICATIONS

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  • Mahmudov Madyarbek Mahmudovich,
  • Ovezov Halmuhammet Amanmuhammedovich
Mahmudov Madyarbek Mahmudovich
Oguz han Engineering and Technology university of Turkmenistan. Ashgabat, Turkmenistan
Ovezov Halmuhammet Amanmuhammedovich
Oguz han Engineering and Technology university of Turkmenistan. Ashgabat, Turkmenistan

Опубликован 25.03.2025

Как цитировать

M.M. Mahmudov, & H.A. Ovezov. (2025). EIGENVALUES OF REGULAR GRAPHS: KEY PROPERTIES, EXAMPLES, AND APPLICATIONS. ОБРАЗОВАНИЕ И НАУКА В XXI ВЕКЕ, 59-4 (том 1). https://mpcareer-google.ru/index.php/journal/article/view/1237

Аннотация

Regular graphs, where each vertex has an identical degree \( d \), are fundamental in graph theory and network science. Their spectral properties—specifically eigenvalues of the adjacency matrix—reveal critical insights into connectivity, expansion, and randomness. This article explores the eigenvalues of regular graphs, highlighting theoretical results, illustrative examples, and practical applications.

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Библиографические ссылки

  1. Alon, N. (1986). Eigenvalues and expanders. *Combinatorica*, 6(2), 83–96.
  2. Hoory, S., Linial, N., & Wigderson, A. (2006). Expander graphs and their applications. *Bulletin of the AMS*, 43(4), 439–561.
  3. Lubotzky, A., Phillips, R., & Sarnak, P. (1988). Ramanujan graphs. *Combinatorica*, 8(3), 261–277.