University of Guilan Journal of Algebra and Related Topics 2345-3931 2026 02 10 Some results on the sign domination number of the subdivision of a graph 9434 10.22124/jart.2026.30427.1793 EN A. Abbasi Department of Pure ‎Mathematics,‎ Faculty of Mathematical Sciences‎,‎ University of Guilan‎,‎‎ ‎‎Rasht‎, ‎Iran K. Mirasheh Department of Pure ‎Mathematics,‎ Faculty of Mathematical Sciences‎,‎ University of Guilan‎,‎‎ ‎‎Rasht‎, ‎Iran E. Vatandoost Department of Pure Mathematics, Faculty of Science‎,‎ Imam Khomeini International University‎, ‎‎‎‎‎‎‎Qazvin‎, ‎Iran Journal Article 2025 04 19 ‎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)‎. ‎$ https://jart.guilan.ac.ir/article_9434_a0d4705766fba01ff0a03d4952174bf7.pdf