A characterization for fuzzy strong cut vertices and fuzzy strong cut edges

Abstract

Abstract Cut vertices and cut edges are valuable for analyzing connectivity problems in classical graph theory. However, they cannot deal with certain fuzzy problems. In order to solve this problem, this paper introduces the definitions of fuzzy strong cut vertices and fuzzy strong cut edges, and characterizes fuzzy strong cut vertices and fuzzy strong cut edges in fuzzy trees, complete fuzzy graphs, and fuzzy cycles. Finally, practical applications verify the effectiveness of the theory in network stability analysis.