International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4155 2020 2020 Department of Mathematics, SRM TRP Engineering College, Tiruchirappalli-621105, Tamil Nadu, India Duraisamy Duraisamy University of New Mexico, Gallup Campus, NM 87301, USA Florentin Smarandache This paper introduces the novel concept of a Neutrosophic Signed Domination Function (NSDF) of graphs, generalizing classical domination by assigning each vertex a triple-valued influences (truth, indeterminacy, falsity) from {−1, 0, 1}. We define the Neutrosophic Signed Domination Number γns(G) as the optimal weighted sum under neighborhood constraints ensuring net positive influence. Fundamental properties and sharp bounds for general graphs are established. Exact values for γns(G) are determined for paths and cycles. This work bridges neutrosophic logic with domination theory, enabling sophisticated modeling of complex networks with uncertainty. 2026 2026 296 308 10.54216/IJNS.270126 https://www.americaspg.com/articleinfo/21/show/4155