TY - JOUR
ID - 24400
TI - Connected zero forcing sets and connected propagation time of graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Khosravi, Maryam
AU - Rashidi, Saeedeh
AU - Sheikhhosseini, Alemeh
AD - Shahid Bahonar University of Kerman
Y1 - 2020
PY - 2020
VL - 9
IS - 2
SP - 77
EP - 88
KW - zero forcing number
KW - connected zero forcing number
KW - propagation time
DO - 10.22108/toc.2020.115286.1617
N2 - 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. We investigate here 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.
UR - https://toc.ui.ac.ir/article_24400.html
L1 - https://toc.ui.ac.ir/article_24400_dadaf115d1d4fd27c010b9ffd131e531.pdf
ER -