Chapter 46

Minimum Rank, Maximum Nullity, and Zero Forcing Number of Graphs

Shaun M. Fallat

University of Regina

Leslie Hogben

Iowa State University and American Institute of Mathematics

This chapter represents an overview of research related to a notion of the “rank of a graph” and the dual concept known as the “nullity of a graph,” from the point of view of associating a fixed collection of symmetric or Hermitian matrices to a given graph. This topic and related questions have enjoyed a fairly large history within discrete mathematics, and have become very popular among linear algebraists recently, partly based on its connection to certain inverse eigenvalue problems, but also because of the many interesting applications (e.g., to communication ...

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