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• # Artykuł - szczegóły

2014 | 2 | 1 |

## On the Relationships between Zero Forcing Numbers and Certain Graph Coverings

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### Abstrakty

EN
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.

EN

wydano
2014-01-01
otrzymano
2013-10-25
zaakceptowano
2014-03-12
online
2014-04-24

### Twórcy

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

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