# Connected zero forcing sets and connected propagation time of graphs

Document Type: Research Paper

Authors

Shahid Bahonar University of Kerman

10.22108/toc.2020.115286.1617

Abstract

The zero forcing number $Z(G)$ of a graph $G$
is the minimum cardinality of a set $S$ with colored (black) vertices which forces the set $V(G)$
to be colored (black) after some times. color change rule'': a white vertex is changed to a black
vertex when it is the only white neighbor of a black vertex.
In this case, we say that the black vertex forces the white vertex.
In this paper, we investigate the concept of connected zero forcing set
and connected zero forcing number. We discusses this subject for special graphs and some products of graphs.
Also we introduce the connected propagation
time. Graphs with extreme minimum connected propagation
times and maximum propagation times $|G|-1$ and $|G|-2$ are characterized.

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Main Subjects