Noncommutative distances on graphs: An explicit approach via Birkhoff-James orthogonality

TL;DR

This paper introduces a method to compute noncommutative distances on graphs using Birkhoff-James orthogonality, providing explicit solutions especially for path graphs, advancing the understanding of graph distances in noncommutative settings.

Contribution

The paper offers a novel explicit approach to calculating noncommutative distances on graphs, with a complete characterization for path graphs, bridging linear algebra and graph theory.

Findings

Explicit solutions for noncommutative distances on path graphs

Characterization of solutions using Birkhoff-James orthogonality

Advancement in noncommutative metric computations on graphs

Abstract

We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterization of the solutions is obtained in the case when the underlying graph is a path.