FUZZY NODE CONNECTIVITY OF SOME CLASSES OF GRAPHS

The parameters defining vulnerability in graph theory can be used as an indicator of the service quality over the network, if nodes or links fail. In the field of graph theory, numerous vulnerability parameters have been defined, including toughness, rupture degree, tenacity, integrity, connectivity, and others. Fuzzy graphs, a specific type of graphs, provide a more effective method of modelling real-world problems than other graphs. This is due to the fact that the uncertainties inherent in the problems can be expressed in a more realistic manner through the use of membership values. However, despite this advantage, there has been limited research conducted on the vulnerability parameters in fuzzy graphs. In this paper, the node connectivity parameter for fuzzy wheel graphs, fuzzy cycle graphs, and fuzzy star graphs are researched and some general formulas are obtained. Additionally, the algorithms are given to find the strength of connectedness between any two nodes and the node connectivity of the given fuzzy graph.