Fuzzy, Neutrosophic, and Uncertain Graph Theory: Properties and Applications (II): Uncertain Planar Graph Theory

This book develops a systematic and unified framework for the study of planar graph theory under uncertainty, integrating classical graph-theoretic concepts with fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and uncertain graph models. The work revisits foundational graph classes—including planar, outerplanar, apex, quasi-planar, and related graph structures—and extends them into uncertainty-aware environments where vertices and edges may carry graded, indeterminate, or attribute-dependent information. Special attention is given to fuzzy planar graphs, intuitionistic fuzzy planar graphs, neutrosophic planar graphs, plithogenic planar graphs, and uncertain planar graph formulations, emphasizing both structural consistency and model-independent interpretations of planarity. In addition, the book explores related extensions to hypergraphs and SuperHyperGraphs, thereby broadening the conceptual landscape of planar structures in higher-order settings. By combining rigorous definitions, examples, comparative perspectives, and theoretical analysis, the book establishes a coherent foundation for future investigations in uncertain network modeling, graph theory, artificial intelligence, graph neural networks, computer vision, VLSI design, and complex systems analysis.