On Eigenvalues Related to Finite Poincaré Planes

LetFqbe a finite field withqelements (qodd). Fix a nonsquare element δ Fq:Hq=Fq( ) −Fq= {x+y x,y≠ 0 Fq} is called a finite Poincaré plane (FPP). The graph structure can be defined on an FPP. This paper studies eigenvalues of the adjacency matrix of an FPP and the distribution of eigenvalues of adjacency matrices of all FPPs.