YULDUZ GRAFASIDAGI SEIDEL AVTOMORFIZMLARI
##article.subject##:
graf, Cayley graf, Star graf, avtomorfizm, Seidel avtomorfizmi, involyutsiya##article.abstract##
Ushbu maqolada Cayley graflar oilasining involyutsiyalari xususiyatlarini simmetrik guruhda o'rganishga bag'ishlangan bo'lib, ularning to'plami faqat ma'lum bir turning transpozitsiyalaridan iborat. Ushbu maqolada quyidagi natijalar olingan: Star grafining Seidel involyutsiyasi bo'lishi uchun zaruriy sharti topilgan, Star grafining barcha avtomorfizmlari 3 ≤ n ≤ 5 da topilgan. Seidelning barcha involyutsiyalari olingan, barcha involyutsiya juftliklari (πl, πr), 3≤ n ≤ 5 da topilgan.
Библиографические ссылки
Е. В. Константинова. Комбинаторные задачи на графах Кэли: учебное пособие. – Новосибирск, РИЦ НГУ. – 2014. – 164с.
S. Lakshmivarahan S., J. S. Jwo, S. K. Dhall. Symmetry in interconnection networks based on Cayley graphs of permutation groups: a survey. // Parallel Comput. – V. 19. – 1993. – P. 361–407.
S. B. Akers, B. Krishnamurthy. A group-theoretic model for symmetric interconnection networks. // IEEE Trans. Comput. – V. 38.
– 1989. P. 555–566.
J. S. Jwo, S. Lakshmivarahan, S. K. Dhall. Embedding of cycles and grids in star graphs. // J. Circuits Syst. Comput. – V. 1. – 1991. – P. 43–74.
S. Goryainov, E. V. Konstantinova, H. Li, D. Zhao. Integral graphs obtained by dual Seidel switching. // Linear Algebra and its Applications. – V. 604. – 2020. – P. 476–489.
Y.-Q. Feng. Automorphism groups of Cayley graphs on symmetric groups with generating transposition sets. // Journal of Combinatorial Theory, Series B. – V. 96. – 2006. – P. 67—72.
F. Harary F, A. J. Schwenk. Which graphs have integral spectra? // Graphs and Combinatorics. – V. 390. – 1974. – P. 45–51.
D. Cvetkovi´c. Cubic integral graphs. // Univ. Beograd. Publ. Fak. Ser. Mat. Fiz. – V. 498/541. – 1975. – P. 107–113.
F. C. Bussemaker, D. Cvetkovi´c. There are exactly 13 connected cubic integral graphs. // Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. – V. 544/576. – 1976. – P. 43–48.
A. J. Schwenk. Exactly thirteen connected cubic graphs have integral spectra. // Lecture Notes in Mathematics. – V. 642. – 1978.
– P. 516–533.
D. Stevanovi´c. Nonexistence of some 4-regular integral graphs. // Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. – V. 10. – 1999. – P. 81–86.
D. Stevanovi´c. 4-regular integral graphs avoiding 3 in the spectrum. // Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. – V. 14. – 2003. – P. 99–110.
D. Stevanovi´c, N. M. M. de Abreu, M. A. A. de Freitas and R. Del- Vecchio. Walks and regular integral graphs. // Linear Algebra Appl.
– V. 423. – 2007. – P. 119–135.
M. Minchenko, I. M. Wanless. Quartic integral Cayley graphs. // Ars Mathematica Contemporanea. – V. 8. – 2015. P. 381–408.
W. H. Haemers. Dual Seidel switching. // Papers dedicated to
J. J. Seidel, P. J. de Doelder, J. de Graaf, and J. H. van Lint (Editors), EUT Report 84-WSK-03, Eindhoven University of Technology, The Netherlands, 1984, pp. 183–190.
А. Г. Курош. Курс высшей алгебры. // Наука. – 1968.
