danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"dan-135Research ArticleМАТЕМАТИКАMATHEMATICSДОСТАТОЧНОЕ СПЕКТРАЛЬНОЕ УСЛОВИЕ ГАМИЛЬТОНОВОСТИ ГРАФАSUFFICIENT SPECTRAL CONDITION FOR HAMILTONICITY OF A GRAPHБЕНЕДИКТОВИЧВ. И.BENEDIKTOVICHV. I.vbened@im.bas-net.byИнститут математики НАН Беларуси, МинскInstitute of Mathematics of the National Academy of Sciences of Belarus, Minsk201506062016595512Copyright © БЕНЕДИКТОВИЧ В.И., 20162016БЕНЕДИКТОВИЧ В.И.BENEDIKTOVICH V.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/135
В данной работе доказывается достаточное условие гамильтоновости графа.
In this article the sufficient spectral condition for Hamiltonicity of a graph has been proved.
спектральный радиусгамильтонов циклгамильтонова цепьминимальная степеньSpectral radiusHamiltonian cycleHamiltonian pathminimum degreeReferencesBrualdi, R. A. On the spectral radius of complementary acyclic matrices of zeros and ones / R. A. Brualdi, E. S. Solheid // SIAM J. Algebraic Discrete Methods. – 1986. – Vol. 7, N 2. – P. 265–272.Brualdi, R. A. On the spectral radius of complementary acyclic matrices of zeros and ones / R. A. Brualdi, E. S. Solheid // SIAM J. Algebraic Discrete Methods. – 1986. – Vol. 7, N 2. – P. 265–272.Fiedler, M. Spectral radius and Hamiltonicity of graphs / M. Fiedler, V. Nikiforov // Linear Algebra Appl. – 2010. – Vol. 432. – P. 2170–2173.Fiedler, M. Spectral radius and Hamiltonicity of graphs / M. Fiedler, V. Nikiforov // Linear Algebra Appl. – 2010. – Vol. 432. – P. 2170–2173.Lu, M. Spectral radius and Hamiltonian graphs / M. Lu, H. Liu, F. Tian // Linear Algebra Appl. – 2012. – Vol. 437. – P. 2670–2741.Lu, M. Spectral radius and Hamiltonian graphs / M. Lu, H. Liu, F. Tian // Linear Algebra Appl. – 2012. – Vol. 437. – P. 2670–2741.Nikiforov, V. The spectral radius of graphs without paths and cycles of specified length / V. Nikiforov // Linear Algebra Appl. – 2010. – Vol. 432. – P. 2243–2256.Nikiforov, V. The spectral radius of graphs without paths and cycles of specified length / V. Nikiforov // Linear Algebra Appl. – 2010. – Vol. 432. – P. 2243–2256.Yuan, W. On the spectral radii of graphs without given cycles / W. Yuan, B. Wang, M. Zhai // Electron. J. Linear Algebra. – 2012. – Vol. 23. – P. 599–606.Yuan, W. On the spectral radii of graphs without given cycles / W. Yuan, B. Wang, M. Zhai // Electron. J. Linear Algebra. – 2012. – Vol. 23. – P. 599–606.Krivelevich, M. Spase pseudo-random graphs are Hamiltonian / M. Krivelevich, B. Sudakov // J. Graph Theory. – 2003. – Vol. 42, N 1. – P. 17–33.Krivelevich, M. Spase pseudo-random graphs are Hamiltonian / M. Krivelevich, B. Sudakov // J. Graph Theory. – 2003. – Vol. 42, N 1. – P. 17–33.Mohar, B. A domain monotonicity theorem for graphs and hamiltonicity / B. Mohar // Discrete Appl. Math. – 1992. – Vol. 36, N 2. – P. 169–177.Mohar, B. A domain monotonicity theorem for graphs and hamiltonicity / B. Mohar // Discrete Appl. Math. – 1992. – Vol. 36, N 2. – P. 169–177.Ning, B. Spectral radius and Hamiltonian properties of graphs / B. Ning, J. Ge // Linear and Multilinear Algebra. – 2014. – Vol. 63, N 8. – P. 1520–1530.Ning, B. Spectral radius and Hamiltonian properties of graphs / B. Ning, J. Ge // Linear and Multilinear Algebra. – 2014. – Vol. 63, N 8. – P. 1520–1530.Hong, Y. A sharp upper bound of the spectral radius of graphs / Y. Hong, J. Shu, K. Fang // J. Combin. Theory. – 2001. – Vol. 81. – P. 177–183.Hong, Y. A sharp upper bound of the spectral radius of graphs / Y. Hong, J. Shu, K. Fang // J. Combin. Theory. – 2001. – Vol. 81. – P. 177–183.Лекции по теории графов / В. А. Емеличев [и др.]. – М.: Наука, 1990.Лекции по теории графов / В. А. Емеличев [и др.]. – М.: Наука, 1990.Brouwer, A. E. Spectra of graphs / A. E. Brouwer, W. H. Haemers. – Springer–Verlag, 2011.Brouwer, A. E. Spectra of graphs / A. E. Brouwer, W. H. Haemers. – Springer–Verlag, 2011.Прасолов, В. В. Многочлены / В. В. Прасолов. – М.: МЦНМО, 2001.Прасолов, В. В. Многочлены / В. В. Прасолов. – М.: МЦНМО, 2001.
The authors declare that there are no conflicts of interest present.