Disjunctive domination in maximal outerplanar graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917981821337600 |
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| author | Henning, Michael A. Maniya, Paras Vinubhai Pradhan, Dinabandhu |
| author_facet | Henning, Michael A. Maniya, Paras Vinubhai Pradhan, Dinabandhu |
| contents | A disjunctive dominating set of a graph $G$ is a set $D \subseteq V(G)$ such that every vertex in $V(G)\setminus D$ has a neighbor in $D$ or has at least two vertices in $D$ at distance $2$ from it. The disjunctive domination number of $G$, denoted by $γ_2^d(G)$, is the minimum cardinality of a disjunctive dominating set of $G$. In this paper, we show that if $G$ is a maximal outerplanar graph of order $n \ge 7$ with $k$ vertices of degree $2$, then $γ_2^d(G)\le \lfloor\frac{2}{9}(n+k)\rfloor$, and this bound is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disjunctive domination in maximal outerplanar graphs Henning, Michael A. Maniya, Paras Vinubhai Pradhan, Dinabandhu Combinatorics Discrete Mathematics 05C69 A disjunctive dominating set of a graph $G$ is a set $D \subseteq V(G)$ such that every vertex in $V(G)\setminus D$ has a neighbor in $D$ or has at least two vertices in $D$ at distance $2$ from it. The disjunctive domination number of $G$, denoted by $γ_2^d(G)$, is the minimum cardinality of a disjunctive dominating set of $G$. In this paper, we show that if $G$ is a maximal outerplanar graph of order $n \ge 7$ with $k$ vertices of degree $2$, then $γ_2^d(G)\le \lfloor\frac{2}{9}(n+k)\rfloor$, and this bound is sharp. |
| title | Disjunctive domination in maximal outerplanar graphs |
| topic | Combinatorics Discrete Mathematics 05C69 |
| url | https://arxiv.org/abs/2504.07186 |