2025/04/16 by Greaves, Gary R. W., Tan, Zhao Kuang
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.12026
Using cyclotomy, we construct a new infinite family of Neumaier graphs that includes infinitely many strongly regular graphs. Notably, this family conjecturally contains infinitely many graphs with coherent rank 6. Our construction also provides the first known examples that answer a question posed by Evans, Goryainov, and Panasenko regarding the existence of Neumaier graphs whose nexus is not a power of 2. In addition, we show that a construction of Greaves and Koolen yields an infinite family of Neumaier graphs with coherent rank 6.