Computing the minimum rank of a loop directed tree

TL;DR

This paper introduces a polynomial-time algorithm to compute the minimum rank of directed trees with loops, extending existing methods from undirected trees to a broader class of graphs.

Contribution

It presents the first efficient algorithm for determining the minimum rank of looped directed trees, expanding the scope of graph classes with known polynomial solutions.

Findings

Algorithm computes minimum rank in polynomial time

Extends minimum rank computation from undirected to directed trees with loops

Demonstrates efficiency and correctness of the proposed method

Abstract

The minimum rank of a graph is the minimum possible rank of a real matrix whose zero-nonzero pattern is described by the graph. The current algorithms can compute efficiently the minimum rank of undirected trees. This paper provides an algorithm to compute in polynomial time the minimum rank of directed trees allowing loops.