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On the $k$-dominating number of Cartesian products of two paths

In: Mathematica Slovaca, vol. 55, no. 2
Antoaneta Klobučar

Details:

Year, pages: 2005, 141 - 154
About article:
A subset $D \subset V(G)$ is called a $k$@-dominating set, $k≥ 1$, if for every vertex $y$ not in $D$, there exists at least one vertex $x \in D$ such that $d(x,y)≤ k$. For convenience we also say that $D$ $k$@-dominates $G$. The $k$@-domination numberk(G)$ is the cardinality of a smallest $k$@-dominating set. The $1$@-domination number is also called the domination number. In this paper we determine the exact values of $γk(P1\mathbin{\square} Pn),…,γk(P3\mathbin{\square} Pn)$, $2$@-domination numbers $γ2(P4\mathbin{\square} Pn),…,γ2(P7\mathbin{\square} Pn)$, estimates for $γk (Pm \mathbin{\square} Pn)$ when $k ≥ m-1$ and $\limm,n\to∞\frac{γk(Pm\mathbin{\square} Pn)}{mn}$ where $Pn$ denote the path of length $n$.
How to cite:
ISO 690:
Klobučar, A. 2005. On the $k$-dominating number of Cartesian products of two paths. In Mathematica Slovaca, vol. 55, no.2, pp. 141-154. 0139-9918.

APA:
Klobučar, A. (2005). On the $k$-dominating number of Cartesian products of two paths. Mathematica Slovaca, 55(2), 141-154. 0139-9918.