On the Relationship Between the Zero Forcing Number and Path Cover Number for Some Graphs

Abstract

The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter bounds the path cover number which is the minimum number of vertex-disjoint-induced paths that cover all the vertices of graph. In this paper, we investigate these two parameters and present an infinite number of graphs with the large difference between these two parameters and an infinite number of graphs with no difference between these parameters. Also, we prove a conjecture about the relationship between these parameters for some graphs.

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Correspondence to Nasrin Soltankhah.

Communicated by Hamid Reza Ebrahimi Vishki.

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Montazeri, Z., Soltankhah, N. On the Relationship Between the Zero Forcing Number and Path Cover Number for Some Graphs. Bull. Iran. Math. Soc. 46, 767–776 (2020). https://doi.org/10.1007/s41980-019-00290-8

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• DOI: https://doi.org/10.1007/s41980-019-00290-8

Keywords

• Zero forcing number
• Path cover number
• Rook’s graph

• 05C70
• 05C75
• 05C76