Jacob
First Name
Bonnie
Last Name
Jacob
Department
Science and Mathematics
Scholarship Year
2025
Research Center
Non-Center Based
Scholarship Type
Journal Paper
Contributors List
Bonnie C. Jacob
Project Title
Well-failed graphs
Start Date - Month
June
Start Date - Year
2021
End Date Anticipated - Month
May
End Date Anticipated - Year
2024
End Date Actual - Month
May
End Date Actual - Year
2025
Review Types
Blind Peer Reviewed
Student Assistance
None
Projected Cost
$0.00
Funding Source
Operating Budget
Resulting Product
peer-reviewed journal article
Citation

Jacob, Bonnie C. "Well-failed graphs." Australasian Journal of Combinatorics 93. 2 (2025): 359-374. Web. *

Abstract

In this paper we begin the study of well-failed graphs, that is, graphs in which every maximal failed zero forcing set is a maximum failed zero forcing set, or equivalently, in which every minimal fort is a minimum fort. We characterize trees that are well-failed. Along the way, we prove that the set of vertices in a graph that are not in any minimal fort is identical to the set of vertices that are in no minimal zero forcing set, which allows us to characterize vertices in a tree that are in no minimal fort.

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