**Speaker**: Sergey Goryainov, Shanghai Jiao Tong University

**Date**: Thu, Jan 18, 2018

**Time**: 14:00 - 15:00

**Venue**: Middle Meeting Room

**Title**: On eigenfunctions and maximal cliques of Paley graphs of square order

**Abstract**:

In Paley graphs of order $q^2$, where $q$ is an odd prime power, we find new maximal cliques of size $\frac{q+1}{2}$ or $\frac{q+3}{2}$, accordingly as $q\equiv 1(4)$ or $q\equiv 3(4)$. After that we use the new cliques to define a family of eigenfunctions corresponding to both non-principal eigenvalues and having support size $q+1$, which is the minimum possible value by the weight-distribution bound.