Bibliography on Deza graphs

For a bibliography and detailed information on strongly regular graphs see the monograph by A.E. Brouwer and H. Van Maldeghem.

Papers on Deza graphs (that are not strongly regular)

[1] M. Erickson, S. Fernando, W.H. Haemers, D. Hardy, J. Hemmeter, Deza graphs: A generalization of strongly regular graphs, Journal of Combinatorial Designs, 7 (1999) 395–405. doi.org/10.1002/(SICI)1520-6610(1999)7:6<395::AID-JCD1>3.0.CO;2-U
[2] F. Li, Y. Wang, Relative difference sets fixed by inversion and Cayley graphs, Journal of Combinatorial Theory, Series A, 111 (2005) 165–173. doi.org/10.1016/j.jcta.2004.09.007
[3] F. Li, Y. Wang, Subconstituents of symplectic graphs, European Journal of Combinatorics, 29 (2008) 1092–1103. doi.org/10.1016/j.ejc.2007.08.001
[4] G. Ermakova, Two problems in algebraic graph theory, PhD thesis, N.N. Krasovskii Institute of Mathematics and Mechanics (2009) (in Russian). pdf
[5] J. Guo, F. Li, K. Wang, Deza graphs based on symplectic spaces, European Journal of Combinatorics, 31 (2010) 1969–1980. doi.org/10.1016/j.ejc.2010.05.006
[6] V.V. Kabanov, L. Shalaginov, Deza graphs with parameters of lattice graphs, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 16(3) (2010) 117–120 (in Russian). pdf
[7] L. Shalaginov, On Deza graphs with parameters of triangular graphs, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 17(1) (2011) 294–298 (in Russian). pdf
[8] S. Goryainov, L. Shalaginov, On Deza graphs with 14, 15 and 16 vertices, Siberian Electronic Mathematical Reports, 8 (2011) 105–115 (in Russian). pdf
[9] N.D. Zyulyarkina, On the commutation graph of cyclic TI-subgroups in unitary groups, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 18(3) (2012) 119–124 (in Russian). pdf
[10] S. Goryainov, L. Shalaginov, On Deza graphs with triangular and lattice graph complements as parameters, Journal of Applied and Industrial Mathematics, 7(3) (2013) 355–362. doi.org/10.1134/S1990478913030083
[11] Y. Meemark, T. Puirod, Symplectic graphs over finite local rings, European Journal of Combinatorics, 34 (2013) 1114–1124. doi.org/10.1016/j.ejc.2013.03.003
[12] J. Guo, F. Li, K. Wang, More on symplectic graphs modulo pⁿ, Linear Algebra and its Applications, 438(6) (2013) 2651–2660. doi.org/10.1016/j.laa.2012.06.026
[13] Z. Gu, Subconstituents of symplectic graphs modulo pⁿ, Linear Algebra and its Applications, 439(5) (2013) 1321–1329. doi.org/10.1016/j.laa.2013.04.015
[14] Z. Gu, Z. Wan, K. Zhou, Subconstituents of orthogonal graphs of odd characteristic – continued, Linear Algebra and its Applications, 439(10) (2013) 2861–2877. doi.org/10.1016/j.laa.2013.08.010
[15] J. Guo, F. Li, K. Wang, Orthogonal graphs over Galois rings of odd characteristic, European Journal of Combinatorics, 39 (2014) 113–121. doi.org/10.1016/j.ejc.2014.01.002
[16] A.L. Gavrilyuk, S. Goryainov, V.V. Kabanov, On the vertex connectivity of Deza graphs, Proceedings of the Steklov Institute of Mathematics, 285(S1) (2014) 68–77. doi.org/10.1134/S0081543814050071
[17] V.V. Kabanov, A. Mityanina, Strictly Deza line graphs, Proceedings of the Steklov Institute of Mathematics, 285(S1) (2014) 78–90. doi.org/10.1134/S0081543814050083
[18] S. Goryainov, L. Shalaginov, Cayley-Deza graphs on less than 60 vertices, Siberian Electronic Mathematical Reports, 11 (2014) 268–310 (in Russian). pdf
[19] A. Mityanina, On K_1,3-free Deza graphs with diameter greater than 2, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 20(2) (2014) 238–241 (in Russian). pdf
[20] Š. Miklavič, P. Šparl, On extendability of Deza graphs with diameter 2, Discrete Mathematics, 338 (2015) 1416–1423. doi.org/10.1016/j.disc.2015.03.007
[21] M. Ahanjideh, More on the subconstituents of symplectic graphs, Boletim da Sociedade Paranaense de Matematica, 33(2) (2015) 17–30. doi.org/10.5269/bspm.v33i2.22849
[22] S. Goryainov, G. Isakova, V.V. Kabanov, N. Maslova, L. Shalaginov, On Deza graphs with disconnected second neighborhood of a vertex, Proceedings of the Steklov Institute of Mathematics, 297(S1) (2017) 97–107. doi.org/10.1134/S008154381705011X
[23] A. Mityanina, On K_1,3-free strictly Deza graphs, Proceedings of the Steklov Institute of Mathematics, 297(S1) (2017) 159–162. doi.org/10.1134/S0081543817050169
[24] V.V. Kabanov, A. Mityanina, Claw-free strictly Deza graphs, Siberian Electronic Mathematical Reports, 14 (2017) 367–387. doi.org/10.17377/semi.2017.14.030
[25] S. Goryainov, D. Panasenko, On vertex connectivity of Deza graphs with parameters of complements to Seidel graphs, European Journal of Combinatorics, 80 (2019) 143–150. doi.org/10.1016/j.ejc.2018.10.006
[26] V.V. Kabanov, N. Maslova, L. Shalaginov, On strictly Deza graphs with parameters (n, k, k–1, a), European Journal of Combinatorics, 80 (2019) 194–202. doi.org/10.1016/j.ejc.2018.07.011
[27] V.V. Kabanov, L. Shalaginov, Deza graphs with parameters (n, k, k–2, a), Journal of Combinatorial Designs, 28 (2020) 658–669. doi.org/10.1002/jcd.21722
[28] S. Akbari, A.H. Ghodrati, M.A. Hosseinzadeh, V.V. Kabanov, E.V. Konstantinova, L. Shalaginov, Spectra of Deza graphs, Linear and Multilinear Algebra, 70(2) (2020) 310–321. doi.org/10.1080/03081087.2020.1723472
[29] V.V. Kabanov, E.V. Konstantinova, L. Shalaginov, Generalised dual Seidel switching and Deza graphs with strongly regular children, Discrete Mathematics, 344(3) (2021) Article ID 112238. doi.org/10.1016/j.disc.2020.112238
[30] S. Akbari, W.H. Haemers, M.A. Hosseinzadeh, V.V. Kabanov, E.V. Konstantinova, L. Shalaginov, Spectra of strongly Deza graphs, Discrete Mathematics, 344(12) (2021) Article ID 112622. doi.org/10.1016/j.disc.2021.112622
[31] S. Goryainov, D. Panasenko, L. Shalaginov, Enumeration of strictly Deza graphs with at most 21 vertices, Siberian Electronic Mathematical Reports, 18(2) (2021) 1423–1432. doi.org/10.33048/semi.2021.18.107
[32] S.S. Zaw, On strictly Deza graphs derived from the Berlekamp-van Lint-Seidel graph, The Art of Discrete and Applied Mathematics, 4(2) (2021) #P2.01. doi.org/10.26493/2590-9770.1335.2fa
[33] R. Bildanov, V. Panshin, G. Ryabov, On WL-rank and WL-dimension of some Deza circulant graphs, Graphs and Combinatorics, 37 (2021) 2397–2421. doi.org/10.1007/s00373-021-02364-z
[34] S. Goryainov, L. Shalaginov, Deza graphs: a survey and new results, (2021). arxiv.org/abs/2103.00228
[35] D. Churikov, G. Ryabov, On WL-rank of Deza Cayley graphs, Discrete Mathematics, 345(2) (2022) Article ID 112622. doi.org/10.1016/j.disc.2021.112692
[36] L. Tsiovkina, Covers of complete graphs and related association schemes, Journal of Combinatorial Theory, Series A, 191 (2022) Article ID 105646. doi.org/10.1016/j.jcta.2022.105646
[37] S. Sriwongsa, S. Sirisuk, Nonisotropic symplectic graphs over finite commutative rings, AIMS Mathematics, 7(1) (2022) 821–839. doi.org/10.3934/math.2022049
[38] G. Ryabov, L. Shalaginov, On WL-rank and WL-dimension of some Deza dihedrants, Zapiski POMI, 518 (2022) 152–172. pdf
[39] D. Crnković, A. Švob, Self-Orthogonal Codes from Deza Graphs, Normally Regular Digraphs and Deza Digraphs, Graphs and Combinatorics, 40 (2024) Article number 35. doi.org/10.1007/s00373-024-02763-y

Papers on divisible design graphs

[40] M.A. Meulenberg, Divisible design graphs, Master's thesis, Tilburg University (2008). pdf
[41] W.H. Haemers, H. Kharaghani, M.A. Meulenberg, Divisible design graphs, Journal of Combinatorial Theory, Series A, 118 (2011) 978–992. doi.org/10.1016/j.jcta.2010.10.003
[42] D. Crnković, W.H. Haemers, Walk-regular divisible design graphs, Designs, Codes and Cryptography, 72 (2014) 165–175. doi.org/10.1007/s10623-013-9861-0
[43] S. Goryainov, W.H. Haemers, V.V. Kabanov, L. Shalaginov, Deza graphs with parameters (n, k, k–1, a) and β = 1, Journal of Combinatorial Designs, 27 (2019) 188–202. doi.org/10.1002/jcd.21644
[44] V.V. Kabanov, L. Shalaginov, On divisible design Cayley graphs, Art of Discrete and Applied Mathematics, 4(2) (2021) #P2.02. doi.org/10.26493/2590-9770.1340.364
[45] L. Shalaginov, Divisible design graphs with parameters (4n, n+2, n–2, 2, 4, n) and (4n, 3n–2, 3n–6, 2n–2, 4, n), Siberian Electronic Mathematical Reports, 18(2) (2021) 1742–1756. doi.org/10.33048/semi.2021.18.134
[46] D. Panasenko, L. Shalaginov, Classification of divisible design graphs with at most 39 vertices, Journal of Combinatorial Designs, 30(4) (2022) 205–219. doi.org/10.1002/jcd.21818
[47] D. Crnković, A. Švob, New constructions of divisible design Cayley graphs, Graphs and Combinatorics, 38 (2022) Article number 17. doi.org/10.1007/s00373-021-02440-4
[48] D. Panasenko, The vertex connectivity of some classes of divisible design graphs, Siberian Electronic Mathematical Reports, 19(2) (2022) 426–438. pdf
[49] V.V. Kabanov, New versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs, Discrete Mathematics, 345(11) (2022) Article ID 113054. doi.org/10.1016/j.disc.2022.113054
[50] V.V. Kabanov, A new construction of strongly regular graphs with parameters of the complement symplectic graph, The Electronic Journal of Combinatorics, 30(1) (2023) #P1.25. doi.org/10.37236/11343
[51] A.L. Gavrilyuk, V.V. Kabanov, Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique, Designs, Codes and Cryptography, (2023). doi.org/10.1007/s10623-023-01348-9

Papers on Deza digraphs

[52] K. Wang, G. Zhang, A directed version of Deza graphs: Deza digraphs, Australasian Journal of Combinatorics, 28 (2003), 239–244. pdf
[53] Y. Feng, K. Wang, Deza digraphs, European Journal of Combinatorics, 27 (2006) 995–1004. doi.org/10.1016/j.ejc.2005.04.001
[54] F. Li, K. Wang, Deza digraphs II, European Journal of Combinatorics, 29 (2008) 369–378. doi.org/10.1016/j.ejc.2007.02.009
[55] Z. Guo, D. Jia, G. Zhang, Minimum arc-cuts of normally regular digraphs and Deza digraphs, Discrete Mathematics, 345(7) (2022) Article ID 112879. doi.org/10.1016/j.disc.2022.112879
[56] D. Crnković, H. Kharaghani, S. Suda, A. Švob, New constructions of Deza digraphs, International Journal of Group Theory, (2023). doi.org/10.22108/ijgt.2023.136268.1823

Papers on divisible design digraphs

[57] D. Crnković, H. Kharaghani, Divisible Design Digraphs, Algebraic Design Theory and Hadamard Matrices, (2015) 43–60. doi.org/10.1007/978-3-319-17729-8_4
[58] D. Crnković, H. Kharaghani, A. Švob, Divisible design Cayley digraphs, Discrete Mathematics, 343(4) (2020) Article ID 111784. doi.org/10.1016/j.disc.2019.111784
[59] H. Kharaghani, S. Suda, Divisible design digraphs and association schemes, Finite Fields and Their Applications, 69 (2021) Article ID 101763. doi.org/10.1016/j.ffa.2020.101763