q-Analogs of divisible design graphs and Deza graphs

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, Hardy and Hemmeter 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.