Given a projective plane Σ and a polarity θ of Σ, the corresponding polarity graph is the graph whose vertices are the points of Σ, and two distinct points p1 and p2 are adjacent if p1 is incident to p θ 2 in Σ. A well-known example of a polarity graph is the Erdős-Rényi orthogonal polarity graph ERq, which appears frequently in a variety of extremal problems. Eigenvalue methods provide an uppe...
