Searcharxiv⌕ Search

arXiv subjects

Zhao Kuang Tan

Publications and source records attributed to Zhao Kuang Tan.

3 recordsLinked to original sources
arXiv2026

Neumaier graphs of coherent rank five

We construct an infinite family of Neumaier graphs of coherent rank five, answering the existence question at the smallest possible coherent rank beyond the strongly regular case. For every prime power $q\geqslant7$ with $q\equiv3\pmod4$, set $n=q+1$. Each graph in our construction has precisely five distinct eigenvalues, Neumaier parameters \[ \left( n(n-1)(n-3), \frac{n^2(n-3)}2, \frac{n(n^2-n-8)}4; \frac{(n-2)^2}{2}, (n-1)(n-3) \right), \] and its adjacency matrix lies in the Bose--Mesner algebra of the four-class association scheme of Holzmann, Kharaghani, and Suda. Paley Hadamard matrices and Desarguesian mutually orthogonal Latin squares yield an infinite family whose smallest member has parameters $(280,160,96;18,35)$.

math.CO↗
arXiv2025

Neumaier graphs from cyclotomy with small coherent rank

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 $6$.

math.CO↗