Some results on the sign domination number of the subdivision of a graph

Abbasi, A.; Mirasheh, K.; Vatandoost, E.

doi:10.22124/jart.2026.30427.1793

Some results on the sign domination number of the subdivision of a graph

Articles in Press

Document Type : Research Paper

Authors

¹ Department of Pure ‎Mathematics,‎ Faculty of Mathematical Sciences‎,‎ University of Guilan‎,‎‎ ‎‎Rasht‎, ‎Iran

² Department of Pure Mathematics, Faculty of Science‎,‎ Imam Khomeini International University‎, ‎‎‎‎‎‎‎Qazvin‎, ‎Iran

10.22124/jart.2026.30427.1793

Abstract

‎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)‎. ‎$

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