aspg-21-4155-1791468681 20261008141121 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2026 27 1 Duraisamy Kumar Department of Mathematics, SRM TRP Engineering College, Tiruchirappalli-621105, Tamil Nadu, India Florentin Smarandache University of New Mexico, Gallup Campus, NM 87301, USA 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 296 308 4155 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.270126 https://www.americaspg.com/journal/21/article/4155 https://www.americaspg.com/storage/91760712541.pdf