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On the outer-connected reinforcement and bondage problems in bipartite graphs: the algorithmic complexity | ||
| Journal of Algorithms and Computation | ||
| مقاله 6، دوره 51، شماره 2، اسفند 2019، صفحه 63-74 اصل مقاله (269.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2019.75163 | ||
| نویسندگان | ||
| Maliheh Hashemipour1؛ Mohammadreza Hooshmandasl1؛ Ali Shakiba2 | ||
| 1Department of Computer Science, Yazd University, Yazd, Iran. | ||
| 2Department of Computer Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. | ||
| چکیده | ||
| An outer connected dominating(OCD) set of a graph $G=(V,E)$ is a set $\tilde{D} \subseteq V$ such that every vertex not in $S$ is adjacent to a vertex in $S$, and the induced subgraph of $G$ by $V \setminus \tilde{D}$, i.e. $G [V \setminus \tilde{D}]$, is connected. The OCD number of $G$ is the smallest cardinality of an OCD set of $G$. The outer-connected bondage number of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with a larger OCD number. Also, the outer-connected reinforcement number of G is the smallest number of edges whose addition to G results in a graph with a smaller OCD number. In 2018, Hashemi et al. demonstrated that the decision problems for the Outer-Connected Bondage and the Outer-Connected Reinforcement numbers are all NP-hard in general graphs. In this paper, we improve these results and show their hardness for bipartite graphs. Also, we obtain bounds for the outer-connected bondage number. | ||
| کلیدواژهها | ||
| Bipartite graphs؛ Outer-connected domination؛ Bondage؛ Reinforcement؛ Complexity | ||
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آمار تعداد مشاهده مقاله: 419 تعداد دریافت فایل اصل مقاله: 338 |
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