Maximum nullity, zero forcing number and propagation time of $\ell$-path graphs
محورهای موضوعی : Combinatorics, Graph theory
F. ‎Kheirydoost
1
(Department of Mathematics, Imam Khomeini International University,
P.O. Box 34149-16818, Qazvin, Iran)
E. Vatandoost
2
(Department of Mathematics, Imam Khomeini International University,
P.O. Box 34149-16818, Qazvin, Iran)
A. Bahraini
3
(Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran)
کلید واژه: Propagation time, zero forcing number, maximum nullity, minimum Rank,
چکیده مقاله :
Let $G$ be a graph with each vertex is colored either white or black. A white vertex is changed to a black vertex when it is the only white neighbor of a black vertex (color-change rule). A zero forcing set $S$ of a graph $G$ is a subset of vertices $G$ with black vertices, all other vertices $G$ are white, such that after finitely many applications of the color-change rule all of vertices $G$ becomes black. The zero forcing number of $G$ is the minimum cardinality of a zero forcing set in $G$, denoted by $Z(G).$ In this paper, we define $\ell-$Path graphs. We give some $\ell-$Path and $\ell-$Ciclo graphs such that their maximum nullity are equal to their zero forcing number. Also, we obtain minimum propagation time and maximum propagation time for them.
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