Maximum nullity‎, ‎zero forcing number and propagation time of $\ell$-path graphs

Journal of Linear and Topological Algebra

دوره 12، شماره 03، دی 2023، صفحه 225-234   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.707863

نویسندگان

F. ‎Kheirydoost¹؛ E. Vatandoost^{* 1}؛ A. Bahraini²

¹Department of Mathematics‎, ‎Imam Khomeini International University‎, ‎P.O‎. ‎Box 34149-16818‎, ‎Qazvin‎, ‎Iran

²Department of Mathematics‎, ‎Islamic Azad University‎, ‎Central Tehran Branch‎, ‎Tehran‎, ‎Iran

چکیده

‎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.

کلیدواژه‌ها

Propagation time؛ zero forcing number؛ maximum nullity؛ minimum Rank

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