@article {
author = {Alishahi, M. and Rezaei-Sani, E.},
title = {GRAPHS WITH TOTAL FORCING NUMBER TWO, REVISITED},
journal = {Journal of Algebraic Systems},
volume = {9},
number = {1},
pages = {53-60},
year = {2021},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2020.9229.1451},
abstract = {A subset of the vertex set of a graph $G$ is called a zero forcing set if by considering them colored and, as far as possible, a colored vertex with exactly one non-colored neighbor forces its non-colored neighbor to get colored, then the whole vertices of $G$ become colored. The total forcing number of a graph $G$, denoted by $F_t(G)$, is the cardinality of a smallest zero forcing set of $G$ which induces a subgraph with no isolated vertex. The connected forcing number, denoted by $F_c(G)$, is the cardinality of a smallest zero forcing set of $G$ which induces a connected subgraph. In this paper, we first characterize the graphs with $F_t(G)=2$ and, as a corollary, we characterize the graphs with $F_c(G)=2$.},
keywords = {Zero forcing set,Total forcing number,Connected forcing number},
url = {https://jas.shahroodut.ac.ir/article_2054.html},
eprint = {https://jas.shahroodut.ac.ir/article_2054_f054a10538ec58a6a4782c9d7458d295.pdf}
}