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There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both… Expand Zero forcing is a graph propagation process introduced in quantum physics and theoretical computer science, and closely related… Expand Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices… 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