A Novel NeutroGraph Model for Dynamic Systems: Advancing NeutroStructures with Partially False Axioms in Interactive Digital Installation Art Design

This paper introduces NeutroGraph, an innovative mathematical model rooted in NeutroStructures, designed to analyze dynamic systems where relational axioms are partially true, indeterminate, and false. Unlike Neutrosophic Graphs, which assign truth, indeterminacy, and falsehood triplets to nodes and edges, a NeutroGraph is defined by at least one NeutroAxiom that is partially false, as outlined in NeutroAlgebra [1,2]. We present a rigorous framework with new metrics, including the NeutroStability Index, NeutroCoherence Degree, and Temporal NeutroFlux, supported by extensive mathematical formulations. The model is applied to a social interaction network, demonstrating its ability to capture axiom partiality. Step-by-step originality is highlighted through novel axioms, metrics, and applications, distinguishing this work from existing graph models. Comparisons with classical, fuzzy, and Neutrosophic Graphs underscore the NeutroGraph's superior handling of real-world complexities, making it a significant contribution to mathematical logic.