vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2025-61-2-106-117vestifm-836Research ArticleМАТЕМАТИКАMATHEMATICSИзопериметрический профиль и резистивные диаметры графов Кэли на симметрической группе с порождающими множествами КоксетераIsoperimetric profile and resistance diameters of Cayley graphs on symmetric groups with Coxeter generating setsВаськовскийМ. М.VaskouskiM. M.

Васьковский Максим Михайлович – доктор физико-математических наук, профессор, заведующий кафедрой ФМИС

пр. Независимости, 4, 220030, Минск

Maksim M. Vaskouski – Dr. Sc. (Physics and Mathematics), Professor, Head of the Higher Mathematics Department

4, Nezavisimosti Ave., 220030, Minsk

vaskovskii@bsu.byЗадорожнюкА. О.ZadarazhniukH. A.

Задорожнюк Анна Олеговна – кандидат физико- математических наук, доцент кафедры ФМИС

пр. Независимости, 4, 220030, Минск

Hanna A. Zadarazhniuk – Ph. D. (Physics and Mathematics), Associate Professor of the Higher Mathematics Department

4, Nezavisimosti Ave., 220030, Minsk

a_zadorozhnuyk@mail.ruГонимарА. В.HanimarA. U.

Гонимар Алексей Владимирович – студент

пр. Независимости, 4, 220030, Минск

Aleksey U. Hanimar – Student

4, Nezavisimosti Ave., 220030, Minsk

Белорусский государственный университетBelarusian State University202511072025612106117Copyright © Васьковский М.М., Задорожнюк А.О., Гонимар А.В., 20252025Васьковский М.М., Задорожнюк А.О., Гонимар А.В.Vaskouski M.M., Zadarazhniuk H.A., Hanimar A.U.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/836

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резистивное расстояниеграф Кэли пузырьковой сортировкиизопериметрические неравенствапостоянная Чигераesistance distancebubble-sort Cayley graphisoperimetric inequalitiesCheeger constantReferencesKrebs M., Shaneen A. Expander Families and Cayley Graphs. Oxford University Press, 2011. 288 p.Krebs M., Shaneen A. Expander Families and Cayley Graphs. Oxford University Press, 2011. 288 p.Lyons R., Peres Y. Probability on Trees and Networks, Cambridge University Press, 2016. 699 p. http://doi.org/10.1017/9781316672815Lyons R., Peres Y. Probability on Trees and Networks, Cambridge University Press, 2016. 699 p. http://doi.org/10.1017/9781316672815Klartag B., Kozma G., Ralli P., Tetali P. Discrete curvature and abelian groups. Canadian Journal of Mathematics, 2016, vol. 6, no. 3, pp. 655–674. https://doi.org/10.4153/CJM-2015-046-8Klartag B., Kozma G., Ralli P., Tetali P. Discrete curvature and abelian groups. Canadian Journal of Mathematics, 2016, vol. 6, no. 3, pp. 655–674. https://doi.org/10.4153/CJM-2015-046-8Chung F. Four proofs for the cheeger inequality and graph partition algorithms. AMS/IP Studies in Advanced Mathematics, 2010, vol. 48, pp. 331–349. https://doi.org/10.1090/amsip/048/17Chung F. Four proofs for the cheeger inequality and graph partition algorithms. AMS/IP Studies in Advanced Mathematics, 2010, vol. 48, pp. 331–349. https://doi.org/10.1090/amsip/048/17Ohring S. R., Sarkar F., Das S. K., Hohndel D. H. Cayley graph connected cycles: a new class of fixed-degree interconnection networks. Proceedings of HICSS’95. Wailea, 1995, pp. 479–488. https://doi.org/10.1109/HICSS.1995.375509Ohring S. R., Sarkar F., Das S. K., Hohndel D. H. Cayley graph connected cycles: a new class of fixed-degree interconnection networks. Proceedings of HICSS’95. Wailea, 1995, pp. 479–488. https://doi.org/10.1109/HICSS.1995.375509Akers S. B., Krishnamurthy B. A group-theoretic model for symmetric interconnection networks. IEEE Transactions on Computers, 1989, vol. 38, no. 4, pp. 555– 565. https://doi.org/10.1109/12.21148Akers S. B., Krishnamurthy B. A group-theoretic model for symmetric interconnection networks. IEEE Transactions on Computers, 1989, vol. 38, no. 4, pp. 555– 565. https://doi.org/10.1109/12.21148Sauerwald T. Randomized Protocols for Information Dissemination. Padeborn, 2008. 150 p.Sauerwald T. Randomized Protocols for Information Dissemination. Padeborn, 2008. 150 p.Heydemann M. C. Cayley graphs and interconnection networks. Graph Symmetry. NATO ASI Series. Dordrecht, Springer, 1997, vol. 497, pp. 167–224. https://doi.org/10.1007/978-94-015-8937-6_5Heydemann M. C. Cayley graphs and interconnection networks. Graph Symmetry. NATO ASI Series. Dordrecht, Springer, 1997, vol. 497, pp. 167–224. https://doi.org/10.1007/978-94-015-8937-6_5Luxburg U., Radl A., Hein M. Hitting and commute times in large random neighbourhood graphs. Journal of Machine Learning Research, 2014, vol. 15, no. 52, pp. 1751– 1798. https://dl.acm.org/doi/10.5555/2627435.2638591Luxburg U., Radl A., Hein M. Hitting and commute times in large random neighbourhood graphs. Journal of Machine Learning Research, 2014, vol. 15, no. 52, pp. 1751– 1798. https://dl.acm.org/doi/10.5555/2627435.2638591Klein D. J., Randic M. Resistance distance. Journal of Mathematical Chemistry, 1993, vol. 12, no. 1, pp. 81–95. https://doi.org/10.1007/BF01164627Klein D. J., Randic M. Resistance distance. Journal of Mathematical Chemistry, 1993, vol. 12, no. 1, pp. 81–95. https://doi.org/10.1007/BF01164627Seshu S., Reed M. B. Linear graphs and electrical networks. Addison-Wesley Publishing Company, 1961. 315 p.Seshu S., Reed M. B. Linear graphs and electrical networks. Addison-Wesley Publishing Company, 1961. 315 p.Gvishiani A. D., Gurvich V. A. Metric and ultrametric spaces of resistances. Russian Mathematical Surveys, 1987, vol. 42, no. 6, pp. 235–236. https://doi.org/10.1070/rm1987v042n06abeh001494Gvishiani A. D., Gurvich V. A. Metric and ultrametric spaces of resistances. Russian Mathematical Surveys, 1987, vol. 42, no. 6, pp. 235–236. https://doi.org/10.1070/rm1987v042n06abeh001494Babai L., Szegedy M. Local expansion of symmetrical graphs. Combinatorics, Probability and Computing, 1992, vol. 1, no. 1, pp. 1–11. https://doi.org/10.1017/S0963548300000031Babai L., Szegedy M. Local expansion of symmetrical graphs. Combinatorics, Probability and Computing, 1992, vol. 1, no. 1, pp. 1–11. https://doi.org/10.1017/S0963548300000031Alahmadi A., Alhazmi H., Ali S., Deza M., Sikiric M. D., Sole P. Hypercube emulation of interconnection networks topologies. Mathematical Methods in Applied Sciences, 2016, vol. 39, no. 16, pp. 4856–4865. https://doi.org/10.1002/mma.3820Alahmadi A., Alhazmi H., Ali S., Deza M., Sikiric M. D., Sole P. Hypercube emulation of interconnection networks topologies. Mathematical Methods in Applied Sciences, 2016, vol. 39, no. 16, pp. 4856–4865. https://doi.org/10.1002/mma.3820Hart S. A note on the edges of the n-cube. Discrete Mathematics, 1976, vol. 14, no. 2, pp. 157–163. https://doi.org/10.1016/0012-365X(76)90058-3Hart S. A note on the edges of the n-cube. Discrete Mathematics, 1976, vol. 14, no. 2, pp. 157–163. https://doi.org/10.1016/0012-365X(76)90058-3Mohar B. Isoperimetric numbers of graphs. Journal of Combinatorial Theory, Series B, 1989, vol. 47, no. 3, pp. 274–291. https://doi.org/10.1016/0095-8956(89)90029-4Mohar B. Isoperimetric numbers of graphs. Journal of Combinatorial Theory, Series B, 1989, vol. 47, no. 3, pp. 274–291. https://doi.org/10.1016/0095-8956(89)90029-4Bollobas B., Leader L. Edge-isoperimetric inequalities in the grid. Combinatorica, 1991, vol. 11, no. 4, pp. 299–314. https://doi.org/10.1007/BF01275667Bollobas B., Leader L. Edge-isoperimetric inequalities in the grid. Combinatorica, 1991, vol. 11, no. 4, pp. 299–314. https://doi.org/10.1007/BF01275667Siconolfi V. Ricci curvature, graphs and eigenvalues. Linear Algebra and its Applications, 2021, vol. 620, pp. 242–267. https://doi.org/10.1016/j.laa.2021.02.026Siconolfi V. Ricci curvature, graphs and eigenvalues. Linear Algebra and its Applications, 2021, vol. 620, pp. 242–267. https://doi.org/10.1016/j.laa.2021.02.026Konstantinova E. Vertex reconstruction in Cayley graphs. Discrete Mathematics, 2009, vol. 309, no. 3, pp. 548–559. https://doi.org/10.1016/j.disc.2008.07.039Konstantinova E. Vertex reconstruction in Cayley graphs. Discrete Mathematics, 2009, vol. 309, no. 3, pp. 548–559. https://doi.org/10.1016/j.disc.2008.07.039Vaskouski M. M., Zadorozhnyuk A. O. Asymptotic behavior of resistance distances in Cayley graphs. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2018, vol. 62, no. 2, pp. 140–146 (in Russian). https://doi.org/10.29235/1561-8323-2018-62-2-140-146Vaskouski M. M., Zadorozhnyuk A. O. Asymptotic behavior of resistance distances in Cayley graphs. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2018, vol. 62, no. 2, pp. 140–146 (in Russian). https://doi.org/10.29235/1561-8323-2018-62-2-140-146Godsil C., Royle G. Algebraic Graph Theory. Springer, 2001. 443 p. https://doi.org/10.1007/978-1-4613-0163-9Godsil C., Royle G. Algebraic Graph Theory. Springer, 2001. 443 p. https://doi.org/10.1007/978-1-4613-0163-9Gould R. Graph Theory. Dover Publications, Inc., 2012. 350 p.Gould R. Graph Theory. Dover Publications, Inc., 2012. 350 p.Atzmon N., Ellis D., Kogan D. An isoperimetric inequality for conjugation invariant sets in the symmetric group. Israel Journal of Mathematics, 2016, vol. 212, no. 1, pp. 139–162. https://doi.org/10.1007/s11856-016-1296-7Atzmon N., Ellis D., Kogan D. An isoperimetric inequality for conjugation invariant sets in the symmetric group. Israel Journal of Mathematics, 2016, vol. 212, no. 1, pp. 139–162. https://doi.org/10.1007/s11856-016-1296-7Benjamini I., Kozma G. A resistance bound via an isoperimetric inequality. Combinatorica, 2005, vol. 25, no. 6, pp. 645–650. https://doi.org/10.1007/s00493-005-0040-4Benjamini I., Kozma G. A resistance bound via an isoperimetric inequality. Combinatorica, 2005, vol. 25, no. 6, pp. 645–650. https://doi.org/10.1007/s00493-005-0040-4Friedman J. On Cayley graphs on the symmetric group generated by transpositions. Combinatorica, 2000, vol. 20, no. 4, pp. 505–519. https://doi.org/10.1007/s004930070004Friedman J. On Cayley graphs on the symmetric group generated by transpositions. Combinatorica, 2000, vol. 20, no. 4, pp. 505–519. https://doi.org/10.1007/s004930070004Kalpakis K., Yesha, Y. On the bisection width of the transposition network. Networks, 1997, vol. 29, no. 1, pp. 69–76. https://doi.org/10.1002/(sici)1097-0037(199701)29:1<69::aid-net7>3.0.co;2-aKalpakis K., Yesha, Y. On the bisection width of the transposition network. Networks, 1997, vol. 29, no. 1, pp. 69–76. https://doi.org/10.1002/(sici)1097-0037(199701)29:1<69::aid-net7>3.0.co;2-aChandra A. K., Raghavan P., Ruzzo W. L., Smolensky R., Tiwari P. The electrical resistance of a graph captures its commute and cover times. Computational Complexity, 1996, vol. 6, no. 4, pp. 312–340. https://doi.org/10.1007/BF01270385Chandra A. K., Raghavan P., Ruzzo W. L., Smolensky R., Tiwari P. The electrical resistance of a graph captures its commute and cover times. Computational Complexity, 1996, vol. 6, no. 4, pp. 312–340. https://doi.org/10.1007/BF01270385Gurvich V. Metric and ultrametric spaces of resistances. Discrete Applied Mathematics, 2010, vol. 158, no. 14, pp. 1496–1505. https://doi.org/10.1016/j.dam.2010.05.007Gurvich V. Metric and ultrametric spaces of resistances. Discrete Applied Mathematics, 2010, vol. 158, no. 14, pp. 1496–1505. https://doi.org/10.1016/j.dam.2010.05.007Vaskouski M., Zadorozhnyuk A. Resistance distances in Cayley graphs on symmetric group. Discrete Applied Mathematics, 2017, vol. 227, pp. 121–135. https:/doi.org/10.1016/j.dam.2017.04.044Vaskouski M., Zadorozhnyuk A. Resistance distances in Cayley graphs on symmetric group. Discrete Applied Mathematics, 2017, vol. 227, pp. 121–135. https:/doi.org/10.1016/j.dam.2017.04.044Kaneko K., Suzuki Y. Node-to-node internally disjoint paths problem in bubble-sort graphs. 10th IEEE Pacific Rim International Symposium on Dependable Computing, 2004. Proceedings, pp. 173–182. https://doi.org/10.1109/PRDC.2004.1276568Kaneko K., Suzuki Y. Node-to-node internally disjoint paths problem in bubble-sort graphs. 10th IEEE Pacific Rim International Symposium on Dependable Computing, 2004. Proceedings, pp. 173–182. https://doi.org/10.1109/PRDC.2004.1276568

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