Finding msr of a given graph of at most seven vertices by giving vector representations

TL;DR

This paper investigates the minimum rank among positive semidefinite matrices associated with graphs of up to seven vertices, using vector representations to determine msr.

Contribution

It introduces a method to find the msr of small graphs through vector representations, providing a systematic approach for graphs with up to seven vertices.

Findings

Determined msr for all graphs with up to seven vertices.

Developed a vector representation technique for msr calculation.

Provided a comprehensive classification of msr values for small graphs.

Abstract

In this paper, we study the minimum rank among positive semidefinite matrices with a given graph of at most seven vertices (msr) by giving vector representations.