Lower bounds for positive semidefinite zero forcing and their applications

Boting Yang ()
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Boting Yang: University of Regina

Journal of Combinatorial Optimization, 2017, vol. 33, issue 1, No 6, 105 pages

Abstract: Abstract The positive semidefinite zero forcing number of a graph is a parameter that is important in the study of minimum rank problems. In this paper, we focus on the algorithmic aspects of computing this parameter. We prove that it is NP-complete to find the positive semidefinite zero forcing number of a given graph, and this problem remains NP-complete even for graphs with maximum vertex degree 7. We present a linear time algorithm for computing the positive semidefinite zero forcing number of generalized series–parallel graphs. We introduce the constrained tree cover number and apply it to improve lower bounds for positive semidefinite zero forcing. We also give formulas for the constrained tree cover number and the tree cover number on graphs with special structures.

Keywords: Zero forcing number; Minimum rank; Tree cover number; Positive semidefinite zero forcing number; Maximum positive semidefinite nullity (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-015-9936-0

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