Grundy dominating sequences and zero forcing sets

Bresar, Bostjan and Bujtás, Csilla and Gologranc, Tanja and Klavzar, Sandi and Kosmrlj, Gasper and Patkós, Balázs and Tuza, Zsolt and Vizer, Máté (2017) Grundy dominating sequences and zero forcing sets. Discrete Optimization. ISSN 1572-5286 (In Press)


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In a graph $G$ a sequence $v_1,v_2,\dots,v_m$ of vertices is Grundy dominating if for all $2\le i \le m$ we have $N[v_i]\not\subseteq \cup_{j=1}^{i-1}N[v_j]$ and is Grundy total dominating if for all $2\le i \le m$ we have $N(v_i)\not\subseteq \cup_{j=1}^{i-1}N(v_j)$. The length of the longest Grundy (total) dominating sequence has been studied by several authors. In this paper we introduce two similar concepts when the requirement on the neighborhoods is changed to $N(v_i)\not\subseteq \cup_{j=1}^{i-1}N[v_j]$ or $N[v_i]\not\subseteq \cup_{j=1}^{i-1}N(v_j)$. In the former case we establish a strong connection to the zero forcing number of a graph, while we determine the complexity of the decision problem in the latter case. We also study the relationships among the four concepts, and discuss their computational complexities.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA166-QA166.245 Graphs theory / gráfelmélet
Depositing User: Balázs Patkós
Date Deposited: 18 Sep 2017 14:25
Last Modified: 18 Sep 2017 14:25

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