Some results concerning the $p$-Royden and $p$-harmonic boundaries of a graph of bounded degree

Abstract

Let p be a real number greater than one and let Γ be a connected graph of bounded degree. We show that the p-Royden boundary of Γ with the p-harmonic boundary removed is an Fσ-set. We also characterize the pharmonic boundary of Γ in terms of the intersection of the extreme points of a certain subset of one-sided infinite paths in Γ.