Modeling Chinese Traditional Cultural Resonance in College Ethnic Instrumental Music Classroom Teaching using Energy driven Bipolar Interval-Valued Neutrosophic Graph

Abstract

 In this work, we present a novel theoretical Neutrosophic framework, termed 
Energy-driven Bipolar Interval-Valued Neutrosophic Graphs (BIVNGs), modeling 
cultural perception dynamics in college ethnic instrumental music education through 
integrating Chinese traditional culture.  As a remedy failure of existing Neutrosophic 
graph (NG) models in capturing composite ambiguity, BIVNGs allow evolving NG by 
integration of interval-valued and bipolar characteristics into graph structures to make 
representation of both supportive and contradictory perceptions. Formal definitions of 
structure and energy of BIVNGs are derived together with their adjacency 
matrices, degree and Laplacian matrices, and propose novel formulations for 
graph energy and Laplacian energy for each of the constituting neutrosophic 
components. We then present case studies from the domain of college ethnic 
instrumental music education to demonstrate the practical utility of the model. 
Through spectral analysis and energy computation, BIVNGs capture and quantify 
the complexity of cultural interactions among student groups, providing a 
powerful mathematical tool for analyzing uncertain and contradictory 
relationships in college ethnic instrumental music education through integrating 
Chinese traditional culture. 

DOI: 10.5281/zenodo.16730047