danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"dan-400Research ArticleМАТЕМАТИКАMATHEMATICSСПЕКТРАЛЬНЫЙ РАДИУС СБАЛАНСИРОВАННОГО ДВУДОЛЬНОГО ГРАФА И ЕГО ГАМИЛЬТОНОВОСТЬSPECTRAL RADIUS OF A BALANCED BIPARTITE GRAPH AND ITS HAMILTONICITYБенедиктовичВ. И.BenediktovichV. I.

канд. физ.-мат. наук, вед. науч. сотрудник

Ph. D. (Physics and Mathematics), Leading researcher

vbened@im.bas-net.byИнститут математики НАН Беларуси, МинскInstitute of Mathematics of the National Academy of Sciences of Belarus, Minsk201728042017612712Copyright © Бенедиктович В.И., 20172017Бенедиктович 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/400

В данной работе получена улучшенная нижняя оценка для спектрального радиуса сбалансированного двудольного графа достаточно большого порядка, дающая условие существования гамильтонового цикла в нем и зависящая от инварианта графа – нижней границы минимальной степени графа.

 

In this article, an improved lower bound for the spectral radius of a balanced bipartite graph of quite a large order giving the condition of existence of a Hamiltonian cycle in it and depending on the lower bound of the minimum degree of the graph has been obtained.

 

матрица смежностиспектральный радиуссбалансированный двудольный графгамильтонов циклминимальная степеньadjacency matrixspectral radiusHamiltonian cycleminimum degreebalanced bipartite graphReferencesOre, O. Arc coverings of graphs / O. Ore // Ann. Mat. Pura Appl. – 1961. – Vol. 55, N 1. – P. 315–321. doi.org/10.1007/ bf02412090.Ore O. Arc coverings of graphs. Annali di Matematica Pura ed Applicata, 1961, vol. 55, no. 1, pp. 315–321. doi. org/10.1007/bf02412090.Ore, O. Hamilton-connected graphs / O. Ore // J. Math. Pures Appl. – 1963. – Vol. 42. – P. 21–27.Ore O. Hamilton-connected graphs. Journal de Mathématiques Pures et Appliquées, 1963, vol. 42, pp. 21–27.Bondy, J. A. A method in graph theory / J. A. Bondy, V. Chvátal // Discrete Math. – 1976. – Vol. 15, N 2. – P. 111–135. doi.org/10.1016/0012-365x(76)90078-9.Bondy J. A., Chvátal V. A method in graph theory. Discrete Mathematics, 1976, vol. 15, no. 2, pp. 111–135. doi. org/10.1016/0012-365x(76)90078-9.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. doi.org/10.1137/0607030.Brualdi R. A., Solheid E. S. On the spectral radius of complementary acyclic matrices of zeros and ones. SIAM Journal on Algebraic Discrete Methods, 1986, vol. 7, no. 2, pp. 265–272. doi.org/10.1137/0607030.Li, B. Spectral analogues of Erdös’ and Moon-Moser’s theorems on Hamilton cycles / B. Li, B. Ning // Linear and Multilinear Algebra. – 2016. – Vol. 64, N 11. – P. 2252–2269. doi.org/10.1080/03081087.2016.1151854.Li B., Ning B. Spectral analogues of Erdös’ and Moon-Moser’s theorems on Hamilton cycles. Linear and Multilinear Algebra, 2016, vol. 64, no. 11, pp. 2252–2269. doi.org/10.1080/03081087.2016.1151854.Kelmans, A. K. On graphs with randomly deleted edges / A. K. Kelmans // Acta Math. Acad. Sci. Hung. – 1981. – Vol. 37, N 1–3. – P. 77–88. doi.org/10.1007/bf01904874.Kelmans A. K. On graphs with randomly deleted edges. Acta Mathematica Academiae Scientiarum Hungaricae, 1981, vol. 37, no. 1–3, pp. 77–88. doi.org/10.1007/bf01904874.Csikvari, P. On a conjecture of V. Nikiforov / P. Csikvari // Discrete Math. – 2009. – Vol. 309, N 13. – P. 4522–4526. doi.org/10.1016/j.disc.2009.02.013.Csikvari P. On a conjecture of V. Nikiforov. Discrete Mathematics, 2009, vol. 309, no. 13, pp. 4522–4526. doi. org/10.1016/j.disc.2009.02.013.Brouwer, A. E. Spectra of graphs / A. E. Brouwer, W. H. Haemers. – New York: Springer-Verlag, 2011. – 255 p.Brouwer A. E., Haemers W. H. Spectra of graphs. New York, Springer-Verlag, 2011. 255 p. doi.org/10.1007/978-1- 4614-1939-6.Godsil, C. D. Algebraic graph theory / C. D. Godsil, G. F. Royle. – New York: Springer-Verlag, 2001. – 442 p.Godsil C. D., Royle G. F. Algebraic graph theory. New York, Springer-Verlag, 2001. 442 p. doi.org/10.1007/978-1- 4613-0163-9.Прасолов, В. В. Многочлены / В. В. Прасолов. – М.: МЦНМО, 2003. – 336 p.Prasolov V. V. Polynomials. Moscow, Moscow Center For Continuous Mathematical Education, 2003. 336 p. (in Russian).Bhattacharya, A. On the first eigenvalue of bipartite Graphs / A. Bhattacharya, S. Friedland, U. N. Peled // The Electronic Journal of Combinatorics. – 2008. – Vol. 15. – P. R144.Bhattacharya A., Friedland S., Peled U. N. On the first eigenvalue of bipartite Graphs. The Electronic Journal of Combinatorics, 2008, vol. 15, pp. R144.

The authors declare that there are no conflicts of interest present.