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This article introduced Bipolar Turiyam Graphs (BTGs), detailing their defining characteristics and key parameters, and established the concept of the Bipolar Turiyam Set (BTS), and examined the significance of Bipolar Relations within these graphs.
The concept of the (α, β, γ, δ)-level graph for a Turiyam graph, a novel extension of fuzzy and neutrosophic graphs that incorporates a fourth independent membership degree representing the unknown or liberal component, is investigated.
Level graphs and strong level graphs are introduced as tools to define and compute the chromatic number of BIFGs, demonstrating that the proposed level-graph method yields exact chromatic numbers for classes of BIFGs.
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