Maximal diameter theorem for directed graphs of positive Ricci curvature

TL;DR

This paper establishes a maximal diameter theorem for directed graphs with positive Ricci curvature, extending previous work on diameter bounds and exploring rigidity conditions for equality cases.

Contribution

It introduces a Cheng-type maximal diameter theorem for directed graphs with positive Ricci curvature, advancing the understanding of geometric properties in discrete settings.

Findings

Proves a Cheng-type maximal diameter theorem for directed graphs.

Characterizes rigidity conditions for the equality case.

Extends diameter comparison results to a maximal diameter context.

Abstract

In a previous work, the authors have introduced a Lin-Lu-Yau type Ricci curvature for directed graphs, and obtained a diameter comparison of Bonnet-Myers type. In this paper, we investigate rigidity properties for the equality case, and conclude a maximal diameter theorem of Cheng type.