A divergence-like characterization of admissible functions on digraphs

Abstract

In previous papers, the author defined a notion of admissible functions for digraphs and studied its properties. The notion of admissible functions naturally comes from the study of mean curvature functions of codimension-one foliations, and admissible functions of foliated manifolds are represented by a divergence formula. In this paper, we show that the similar divergence-like formula characterizes admissible functions of digraphs.