General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph

Graph classes categorize graphs based on shared properties or structures, and numerous such classes have been proposed over time. In 1965, Zadeh [43] introduced a framework for managing uncertainty, which later inspired Rosenfeld [28, 31] to develop fuzzy graph theory in 1975. A Neutrosophic Graph, as a generalization of a Fuzzy Graph, associates each vertex and edge with three membership values representing truth, indeterminacy, and falsity. This allows Neutrosophic Graphs to handle uncertain, vague, or contradictory information more effectively. This paper aims to expand the study of Neutrosophic Graphs by proposing new graph classes, specifically the General-Neutrosophic Graph, Anti-Neutrosophic Graph, *-Balanced-Neutrosophic Graph, and Semi-Neutrosophic Graph.