connected zero forcing sets and connected propagation time of graphs

• DOI: 10.22108/toc.2020.115286.1617
• Publication Date: 2017-01-01
• Authors: Saeedeh Rashidi; Maryam Khosravi; Alemeh Sheikhhoss...
• Keywords: connected zero forcing number; QA1-939; FOS: Mathematics; Mathematics - Combinatorics; 0102 computer and information sciences; Combinatorics (math.CO); propagation time; 0101 mathematics; zero forcing number; 01 natural sciences; Mathematics

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.