The Bipartite Zero Forcing Set for a Full Sign Pattern Matrix

Gu-Fang Mou, Tian-Fei Wang and Zhong-Shan Li
Additional contact information
Gu-Fang Mou: College of Mathematics and Information Science, Leshan Normal University, Leshan 614000, Sichuan, China
Tian-Fei Wang: College of Mathematics and Information Science, Leshan Normal University, Leshan 614000, Sichuan, China
Zhong-Shan Li: Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302-4110, USA

Mathematics, 2020, vol. 8, issue 3, 1-14

Abstract: For an m × n sign pattern P , we define a signed bipartite graph B ( U , V ) with one set of vertices U = { 1 , 2 , … , m } based on rows of P and the other set of vertices V = { 1 ′ , 2 ′ , … , n ′ } based on columns of P . The zero forcing number is an important graph parameter that has been used to study the minimum rank problem of a matrix. In this paper, we introduce a new variant of zero forcing set−bipartite zero forcing set and provide an algorithm for computing the bipartite zero forcing number. The bipartite zero forcing number provides an upper bound for the maximum nullity of a square full sign pattern P . One advantage of the bipartite zero forcing is that it can be applied to study the minimum rank problem for a non-square full sign pattern.

Keywords: signed bipartite graph; bipartite zero forcing; directed constrained matching; minimum rank problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/3/354/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/3/354/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:3:p:354-:d:329041

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().