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arXiv · 2405.13230

$q$-Analogs of divisible design graphs and Deza graphs

Dean Crnkovic·Maarten De Boeck·Francesco Pavese·Andrea Svob
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Abstract

Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of $q$-analogs of divisible design graphs and show that all $q$-analogs of divisible design graphs come from spreads, and are actually $q$-analogs of strongly regular graphs. Deza graphs were introduced by Erickson, Fernando, Haemers and Hardy in 1999. In this paper, we introduce $q$-analogs of Deza graphs. Further, we determine possible parameters, give examples of $q$-analogs of Deza graphs and characterize all non-strongly regular $q$-analogs of Deza graphs with the smallest parameters.

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Dean Crnkovic, Maarten De Boeck, Francesco Pavese, Andrea Svob. 2024-05-21. $q$-Analogs of divisible design graphs and Deza graphs. https://arxiv.org/abs/2405.13230

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