TY - JOUR
ID - 2054
TI - GRAPHS WITH TOTAL FORCING NUMBER TWO, REVISITED
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Alishahi, M.
AU - Rezaei-Sani, E.
AD - Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box:
316-3619995161, Shahrood, Iran.
Y1 - 2021
PY - 2021
VL - 9
IS - 1
SP - 53
EP - 60
KW - Zero forcing set
KW - Total forcing number
KW - Connected forcing number
DO - 10.22044/jas.2020.9229.1451
N2 - 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 $F_c(G)=2$.
UR - https://jas.shahroodut.ac.ir/article_2054.html
L1 - https://jas.shahroodut.ac.ir/article_2054_f054a10538ec58a6a4782c9d7458d295.pdf
ER -