On the Relationships between Zero Forcing Numbers and Certain Graph Coverings-Reference-Cited by-同舟云学术

On the Relationships between Zero Forcing Numbers and Certain Graph Coverings

Published:2014-01-01 Issue:1 Volume:2 Page:
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Taklimi Fatemeh Alinaghipour¹,Fallat Shaun²,Meagher Karen²

Affiliation:

1. Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, S4S 0A4 Regina SK, Canada

2. Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, S4S 0A4 Regina SK, Canada, Research supported by an NSERC Discovery Research Grant.

Abstract

Abstract The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced paths in the graph that cover all the vertices of the graph, while the positive zero forcing number is an upper bound on the minimum number of induced trees in the graph needed to cover all the vertices in the graph. We show that for a block-cycle graph the zero forcing number equals the path cover number.We also give a purely graph theoretical proof that the positive zero forcing number of any outerplanar graphs equals the tree cover number of the graph. These ideas are then extended to the setting of k-trees, where the relationship between the positive zero forcing number and the tree cover number becomes more complex.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.2478/spma-2014-0004/pdf

Reference22 articles.

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