Discrete mathematics, algebraic combinatorics, strongly regular graphs and their generalisations, Cayley graphs, finite fields.

Preprints

• A. Bhowmik, B. De Bruyn, S. Goryainov, Divisible design graphs with selfloops, May 2025. arXiv:2505.03276, submitted to Discrete Mathematics.

• A. E. Brouwer, S. Goryainov, L. Shalaginov, C. H. Yip, Cliques in Paley graphs of square order and in Peisert graphs, March 2025. arXiv:2503.09914 , submitted to European Journal of Combinatorics.

• A. Bhowmik, S. Goryainov, Divisible design graphs from symplectic graphs over rings with precisely three ideals, December 2024. arXiv:2412.04962, submitted to Designs, Codes and Cryptography.

• S. Goryainov, D. Krotov, Completely regular codes in graphs covered by a Hamming graph, November 2024. arXiv:2411.09698

• S. Goryainov, L. V. Shalaginov, Deza graphs: a survey and new results, March 2021. arXiv:2103.00228

Journal publications

1. R. J. Evans, S. Goryainov, L. Shalaginov, Tightness of the weight-distribution bound for strongly regular polar graphs, Journal of Combinatorial Designs, August 2025, doi.org/10.1002/jcd.22001


2. R. J. Evans, A. L. Gavrilyuk, S. Goryainov, K. Vorob'ev, Equitable 2-partitions of the Johnson graphs $J(n,3)$, Discrete Mathematics, Volume 348, Issue 10, October 2025, 114565. doi.org/10.1016/j.disc.2025.114565


3. B. De Bruyn, S. Goryainov, W. H. Haemers, L. Shalaginov, Divisible design graphs from the symplectic graph, Designs, Codes and Cryptography, Volume 93, 1401–1424 (2025). doi.org/10.1007/s10623-024-01557-w


4. S. Goryainov, E. V. Konstantinova, Non-canonical maximum cliques without a design structure in the block graphs of 2-designs, Designs, Codes and Cryptography, 92, 3665–3675 (2024). doi.org/10.1007/s10623-024-01459-x


5. S. Goryainov, D. Panasenko, On eigenfunctions of the block graphs of geometric Steiner systems, Journal of Combinatorial Designs, Volume 32, Issue 11, November 2024, Pages 629-641. doi.org/10.1002/jcd.21951


6. S. Goryainov, C. H. Yip, Extremal Peisert-type graphs without the strict-EKR property, Journal of Combinatorial Theory, Series A, Volume 206, August 2024, 105887. doi.org/10.1016/j.jcta.2024.105887


7. R. J. Evans, S. Goryainov, E. V. Konstantinova, A. D. Mednykh, A general construction of strictly Neumaier graphs and a related switching, Discrete Mathematics, Volume 346, Issue 7, July 2023, 113384. doi.org/10.1016/j.disc.2023.113384


8. S. Goryainov, L. Shalaginov, C. H. Yip, On eigenfunctions and maximal cliques of generalised Paley graphs of square order, Finite Fields and Their Applications, Volume 87, March 2023, 102150. doi.org/10.1016/j.ffa.2022.102150


9. S. Asgarli, S. Goryainov, H. Lin, C. H. Yip, The EKR-module property of pseudo-Paley graphs of square order, The Electronic Journal of Combinatorics, 29(4) (2022), #P4.33. doi.org/10.37236/10962


10. S. Goryainov, A. Masley, L. Shalaginov, On a correspondence between maximal cliques in Paley graphs of square order, Discrete Mathematics, Volume 345, Issue 6, June 2022, 112853. doi.org/10.1016/j.disc.2022.112853


11. S. Goryainov, D. Panasenko, L. Shalaginov, Enumeration of strictly Deza graphs with at most 21 vertices, Siberian Electronic Mathematical Reports, 8(2) (2021), pages 1423-1432. doi.org/10.33048/semi.2021.18.107


12. D. Fan, S. Goryainov, X. Huang, H. Lin, The spanning $k$-trees, perfect matchings and spectral radius of graphs, Linear and Multilinear Algebra, Volume 70, Issue 21, 2022. doi.org/10.1080/03081087.2021.1985055


13. D. Fan, S. Goryainov, H. Lin, On the (signless Laplacian) spectral radius of minimally k-(edge)-connected graphs for small k, Discrete Applied Mathematics, Volume 305, December 2021, pages 154-163. doi.org/10.1016/j.dam.2021.09.002


14. S. V. Goryainov, E. V. Konstantinova, H. Li, D. Zhao, Integral graphs obtained by dual Seidel switching, Linear Algebra and Its Applications, Volume 604, November 2020, pages 476-489. doi.org/10.1016/j.laa.2020.07.010


15. S. V. Goryainov, V. V. Kabanov, E. V. Konstantinova, L. V. Shalaginov, A. A. Valyuzhenich, PI-eigenfunctions of the Star graphs, Linear Algebra and Its Applications, Volume 586, February 2020, pages 7-27. doi.org/10.1016/j.laa.2019.10.018


16. S. V. Goryainov, D. I. Panasenko, On vertex connectivity of Deza graphs with parameters of complements to Seidel graphs, European Journal of Combinatorics, Volume 80, August 2019, pages 143-150. doi.org/10.1016/j.ejc.2018.10.006


17. R. J. Evans, S. V. Goryainov, D. I. Panasenko, The smallest strictly Neumaier graph and its generalisations, The Electronic Journal of Combinatorics, 26(2) (2019), #P2.29. doi.org/10.37236/8189


18. S. V. Goryainov, W. H. Haemers, V. V. Kabanov, L. V. Shalaginov, Deza graphs with parameters $(n,k,k-1,a)$ and $\beta = 1$, Journal of Combinatorial Designs, Volume 27, Issue 3, March 2019, pages 188-202. doi.org/10.1002/jcd.21644


19. R. A. Bailey, P. J. Cameron, A. L. Gavrilyuk, S. V. Goryainov, Equitable partitions of Latin-square graphs, Journal of Combinatorial Designs, Volume 27, Issue 3, March 2019, pages 142-160. doi.org/10.1002/jcd.21634


20. S. V. Goryainov, V. V. Kabanov, L. V. Shalaginov, A. A. Valyuzhenich, On eigenfunctions and maximal cliques of Paley graphs of square order, Finite Fields and Their Applications, Volume 52, pages 361-369, July 2018. doi.org/10.1016/j.ffa.2018.05.001


21. S. V. Goryainov, G. S. Isakova, V. V. Kabanov, N. V. Maslova, L. V. Shalaginov, On Deza graphs with disconnected second neighborhood of a vertex, Proceedings of the Steklov Institute of Mathematics July 2017, Volume 297 Supplement 1, pages 97-107. doi.org/10.1134/S008154381705011X


22. S. V. Goryainov, On isomorphism between distance-regular graphs, Siberian Electronic Mathematical Reports, 11 (2014), pages 311-320. pdf


23. S. V. Goryainov, L. V. Shalaginov, Cayley-Deza graphs, on less than 60 vertices, Siberian Electronic Mathematical Reports, 11 (2014), pages 268-310 (in Russian). pdf


24. A. L. Gavrilyuk, S. V. Goryainov, V. V. Kabanov, On the vertex connectivity of Deza graphs, Proceedings of the Steklov Institute of Mathematics, June 2014, Volume 285, Supplement 1, pages 68-77. doi.org/10.1134/S0081543814050071


25. S. V. Goryainov, L. V. Shalaginov, On Deza graphs with triangular and lattice graph complements as parameters, Applied and Industrial Mathematics, July 2013, Volume 7, Issue 3, pages 355-362. doi.org/10.1134/S1990478913030083


26. A. L. Gavrilyuk, S. V. Goryainov, On perfect 2-colorings of Johnson graphs J(v,3), Journal of Combinatorial Designs, Volume 21, Issue 6, pages 232-252, June 2013. doi.org/10.1002/jcd.21327


27. S. V. Goryainov, L. V. Shalaginov, On Deza graphs with 14, 15 and 16 vertices, Siberian Electronic Mathematical Reports, 8 (2011), pages 105-115 (in Russian). pdf