Zero forcing for sign patterns

2013/07/08 by Felix Goldberg, Goldberg, Felix, Abraham Berman +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1307.2198

arxiv created 2013/07/08 · openalex publication_date 2013/07/08 · arxiv updated 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new variant of zero forcing - signed zero forcing. The classical zero forcing number provides an upper bound on the maximum nullity of a matrix with a given graph (i.e. zero-nonzero pattern). Our new variant provides an analo- gous bound for the maximum nullity of a matrix with a given sign pattern. This allows us to compute, for instance, the maximum nullity of a Z-matrix whose graph is L(K_n), the line graph of a clique.

Citations

• Variants on the minimum rank problem: A survey II

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