Zero forcing number, maximum nullity, and path cover number of subdivided graphs

Thumbnail Image
Catral, Minerva
Cepek, Anna
Huynh, My
Lazebnik, Kirill
Peters, Travis
Young, Michael
Major Professor
Committee Member
Journal Title
Journal ISSN
Volume Title
Hogben, Leslie
Associate Dean
Research Projects
Organizational Units
Organizational Unit
Welcome to the exciting world of mathematics at Iowa State University. From cracking codes to modeling the spread of diseases, our program offers something for everyone. With a wide range of courses and research opportunities, you will have the chance to delve deep into the world of mathematics and discover your own unique talents and interests. Whether you dream of working for a top tech company, teaching at a prestigious university, or pursuing cutting-edge research, join us and discover the limitless potential of mathematics at Iowa State University!
Journal Issue
Is Version Of

The zero forcing number, maximum nullity and path cover number of a (simple, undirected) graph are parameters that are important in the study of minimum rank problems. We investigate the effects on these graph parameters when an edge is subdivided to obtain a so-called edge subdivision graph. An open question raised by Barrett et al. is answered in the negative, and we provide additional evidence for an affirmative answer to another open question in that paper [W. Barrett, R. Bowcutt, M. Cutler, S. Gibelyou, and K. Owens. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530-563, 2009.]. It is shown that there is an independent relationship between the change in maximum nullity and zero forcing number caused by subdividing an edge once. Bounds on the effect of a single edge subdivision on the path cover number are presented, conditions under which the path cover number is preserved are given, and it is shown that the path cover number and the zero forcing number of a complete subdivision graph need not be equal.


This article is published as Catral, Minerva, Anna Cepek, Leslie Hogben, My Huynh, Kirill Lazebnik, Travis Peters, and Michael Young. "Zero forcing number, maximum nullity, and path cover number of subdivided graphs." The Electronic Journal of Linear Algebra 23 (2012): 906-922. DOI: 10.13001/1081-3810.1565. Posted with permission.

Subject Categories
Sun Jan 01 00:00:00 UTC 2012