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

Abstract

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. 

DOI: 10.5281/zenodo.15635413