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Some results on the sign domination number of the subdivision of a graph | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 21 بهمن 1404 اصل مقاله (178.22 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.30427.1793 | ||
| نویسندگان | ||
| A. Abbasi1؛ K. Mirasheh1؛ E. Vatandoost* 2 | ||
| 1Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran | ||
| 2Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran | ||
| چکیده | ||
| We present some new bounds for signed domination numbers. Let $G=(V, E)$ be a simple and undirected graph. For a function $ f : V \longrightarrow \lbrace -1 , 1\rbrace, $ the weight of is $ f $ defined by $ w(f) = \sum_{ v\in V} f(v). $ For a vertex $ v $ in $ V, $ we define $ f [v] = \sum_{u\in N[v]} f(u). $ A signed domination function of $ G $ is a function $ f : V \longrightarrow \lbrace -1 ,1\rbrace $ such that $ f[v] \geq 1 $ for all $ v \in V. $ The signed domination number $ \gamma_{s}(G) $ of $ G $ is the minimum weight among all signed domination functions of $ G. $ In this paper, we study the signed domination problem of the general graph, and obtain some bounds of the signed domination number of $ G. $ We also establish upper and lower bounds of the signed domination number of subdivision construction $ S(G). $ | ||
| کلیدواژهها | ||
| Signed domination؛ Dominating set؛ Subdivision | ||
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آمار تعداد مشاهده مقاله: 9 تعداد دریافت فایل اصل مقاله: 23 |
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