Zero forcing parameters and minimum rank problems
نویسندگان
چکیده
Abstract. The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a 1 graph G, is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by 2 G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive 3 semidefinite zero forcing number Z+(G) is introduced, and shown to be equal to |G| −OS(G), where OS(G) is the 4 recently defined ordered set number that is a lower bound for minimum positive semidefinite rank. The positive 5 semidefinite zero forcing number is applied to the computation of positive semidefinite minimum rank of certain 6 graphs. An example of a graph for which the real positive symmetric semidefinite minimum rank is greater than 7 the complex Hemitian positive semidefinite minimum rank is presented. 8
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