An investigation on fuzzy optimal cut vertices and fuzzy optimal cut edges with their applications

Abstract

Fuzzy graphical models are valuable for analyzing the robustness of networks. Specifically, attacks on certain nodes (edges) in the network can have an avalanche effect on the robustness of the network, and these nodes (edges) correspond to the cut vertices (edges) in the fuzzy graph model. However, the definition of fuzzy cut vertices (edges) ignores the length of paths in a fuzzy graph. To address this flaw, we give the concept of fuzzy optimal cut vertices (edges). In particular, the properties of fuzzy optimal cut vertices (edges) in special fuzzy graphs are explored, and then the corresponding criteria are given. Moreover, we discuss the relations between strong edges, the weakest edges or fuzzy optimal cut vertices and fuzzy optimal cut edges. Finally, the effectiveness of fuzzy optimal cut vertices (edges) in analyzing network robustness is verified by practical examples.

Keywords

• Fuzzy optimal paths
• Fuzzy optimal cut vertices
• Fuzzy optimal cut edges
• Robustness of networks