Minimum rank of a graph

There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both… Expand

The minimum rank problem asks to find the minimum rank over all matrices with a given pattern associated with a graph. This… Expand

This chapter represents an overview of research related to a notion of the “rank of a graph" and the dual concept known as the… Expand

The Minimum Rank Problem for Outerplanar Graphs John H. Sinkovic III Department of Mathematics, BYU Doctor of Philosophy Given a… Expand

Abstract In this paper we introduce a new parameter for a graph called the minimum universal rank. This parameter is similar to… Expand

In this paper we deal with two aspects of the minimum rank of a simple undirected graph $G$ on $n$ vertices over a finite field… Expand

The minimum rank of a simple graph $G$ is defined to be the smallest possible rank over all symmetric real matrices whose $ij$th… Expand

For a field F and graph G of order n, the minimum rank of G over F is defined to be the smallest possible rank over all symmetric… Expand