Deza graphs were introduced in [1]. In [1] the complete list of strictly Deza graphs with at most 13 vertices was presented and different constructions for those graphs were discussed. In [8] this list was extended up to 16 vertices. In [31] the algorithm for enumerating Deza graphs from [8] was reworked and a complete list of strictly Deza graphs up to 21 vertices was obtained. In [18] all Cayley-Deza graphs with a > 0 up to 59 vertices were enumerated.
Divisible design graphs were first studied in master's thesis by M.A. Meulenberg [40] and the list of feasible parameters of divisible design graphs up to 50 vertices was presented. In the following papers [41, 42] divisible design graphs were studied in more details and the existence of graphs was resolved in all but one cases for graphs up to 27 vertices. In [46] the list of all proper divisible design graphs with at most 39 vertices except for three tuples of parameters (32, 15, 6, 7, 4, 8), (32, 17, 8, 9, 4, 8) and (36, 24, 15, 16, 4, 9) was obtained and a mistake from [41, 42] regarding the existence of graphs with parameters (27, 8, 4, 2, 9, 3) was fixed. In [50] a construction that allows to get all graphs with parameters (36, 24, 15, 16, 4, 9) was proposed. In [47] divisible design Cayley graphs up to 27 vertices were classified.
Database of small strictly Deza graphs from [1, 8, 32] can be found
here.
Database of small strictly Cayley-Deza graphs with a > 0 from [18] can be found
here.
Database of small proper divisible design graphs from [46] can be found
here.
References
The numbering of sources is taken from the bibliography.
[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
[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
[18] S. Goryainov, L. Shalaginov, Cayley-Deza graphs on less than 60 vertices, Siberian Electronic Mathematical Reports, 11 (2014) 268–310 (in Russian). pdf
[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
[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
[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
[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