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Divisible design graphs with selfloops

Anwita Bhowmik, Bart De Bruyn (UGent) and Sergey Goryainov
(2026) DISCRETE MATHEMATICS. 349(3).
Author
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Abstract
We develop a basic theory for divisible design graphs with possible selfloops (LDDG's), and describe two infinite families of such graphs, some members of which are also classical examples of divisible design graphs without loops (DDG's). Among the described theoretical results is a discussion of the spectrum, a classification of all examples satisfying certain parameter restrictions or having at most three eigenvalues, a discussion of the structure of the improper and the disconnected examples, and a procedure called dual Seidel switching which allows to construct new examples of LDDG's from others. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keywords
Divisible design graph, Loop, Projective space, Polarity

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Citation

Please use this url to cite or link to this publication:

MLA
Bhowmik, Anwita, et al. “Divisible Design Graphs with Selfloops.” DISCRETE MATHEMATICS, vol. 349, no. 3, 2026, doi:10.1016/j.disc.2025.114824.
APA
Bhowmik, A., De Bruyn, B., & Goryainov, S. (2026). Divisible design graphs with selfloops. DISCRETE MATHEMATICS, 349(3). https://doi.org/10.1016/j.disc.2025.114824
Chicago author-date
Bhowmik, Anwita, Bart De Bruyn, and Sergey Goryainov. 2026. “Divisible Design Graphs with Selfloops.” DISCRETE MATHEMATICS 349 (3). https://doi.org/10.1016/j.disc.2025.114824.
Chicago author-date (all authors)
Bhowmik, Anwita, Bart De Bruyn, and Sergey Goryainov. 2026. “Divisible Design Graphs with Selfloops.” DISCRETE MATHEMATICS 349 (3). doi:10.1016/j.disc.2025.114824.
Vancouver
1.
Bhowmik A, De Bruyn B, Goryainov S. Divisible design graphs with selfloops. DISCRETE MATHEMATICS. 2026;349(3).
IEEE
[1]
A. Bhowmik, B. De Bruyn, and S. Goryainov, “Divisible design graphs with selfloops,” DISCRETE MATHEMATICS, vol. 349, no. 3, 2026.
@article{01KFDT5B1KVXAPTHJXHA9A41NB,
  abstract     = {{We develop a basic theory for divisible design graphs with possible selfloops (LDDG's), and describe two infinite families of such graphs, some members of which are also classical examples of divisible design graphs without loops (DDG's). Among the described theoretical results is a discussion of the spectrum, a classification of all examples satisfying certain parameter restrictions or having at most three eigenvalues, a discussion of the structure of the improper and the disconnected examples, and a procedure called dual Seidel switching which allows to construct new examples of LDDG's from others. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.}},
  articleno    = {{114824}},
  author       = {{Bhowmik, Anwita and De Bruyn, Bart and Goryainov, Sergey}},
  issn         = {{0012-365X}},
  journal      = {{DISCRETE MATHEMATICS}},
  keywords     = {{Divisible design graph,Loop,Projective space,Polarity}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{15}},
  title        = {{Divisible design graphs with selfloops}},
  url          = {{http://doi.org/10.1016/j.disc.2025.114824}},
  volume       = {{349}},
  year         = {{2026}},
}
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