Neutrosophic Signed Domination Function of Graphs
Duraisamy Kumar1,∗, Florentin Smarandache2
1Department of Mathematics, SRM TRP Engineering College, Tiruchirappalli-621105, Tamil Nadu, India
2University of New Mexico, Gallup Campus, NM 87301, USA
Emails: dkumarcnc@gmail.com; fsmarandache@gmail.com
Abstract
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.
Keywords: Graph domination; Neutrosophic graphs; Neutrosophic domination; Signed domination; Neutro-
sophic signed domination