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Stability with respect to total restrained domination in bipartite graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 تیر 1404 اصل مقاله (254.74 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.11697.1113 | ||
| نویسندگان | ||
| Akbar Azami Aghdash1؛ Nader Jafari Rad* 2؛ Bahram Vakili1 | ||
| 1Azad University | ||
| 2Shahed University | ||
| تاریخ دریافت: 09 بهمن 1403، تاریخ پذیرش: 18 اسفند 1403 | ||
| چکیده | ||
| Let $G=(V,E)$ be a graph with no isolated vertices. A subset $D$ of vertices is called a total dominating set (abbreviated TDS) if every vertex of $G$ is adjacent to a vertex in $D$. A TDS $D$ is a total restrained dominating set (abbreviated TRDS) if $D$ has a further property that each vertex outside $D$ is adjacent to a vertex outside $D$. The total restrained domination number of $G$, which we denote it by $\gamma_{tr}(G)$, is the minimum cardinality of a TRDS of $G$. The minimum number of vertices of $G$ whose removal changes the total restrained domination number of $G$ is called the total restrained domination stability number of $G$, and is denoted by $st_{\gamma_{tr}}(G)$. In this paper we study this variant in bipartite graphs. We show that the associated decision problem to this variant is NP-hard even when restricted to bipartite graphs. We also determine the total restrained stability number in some families of graphs, including the families of trees and unicyclic graphs. | ||
| کلیدواژه‌ها | ||
| Total dominating set؛ Total restrained dominating set؛ Bipartite graph | ||
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آمار تعداد مشاهده مقاله: 29 تعداد دریافت فایل اصل مقاله: 39 |
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