The isoperimetric number of the incidence graph of PG(n, q)

Abstract

Let Γn,q be the point-hyperplane incidence graph of the projective space PG(n, q), where n ≥ 2 is an integer and q a prime power. We determine the order of magnitude of 1 − iV (Γn,q), where iV (Γn,q) is the vertex-isoperimetric number of Γn,q. We also obtain the exact values of iV (Γ2,q) and the related incidence-free number of Γ2,q for q ≤ 16.