Algorithms for Computing Pythagorean Fuzzy Average Edge Connectivity of Pythagorean Fuzzy Graphs

Average edge connectivity is a fundamental metric in classical and fuzzy graph theory. It is a key parameter in evaluating the reliability of a network. Fuzzy average edge connectivity more accurately describes the overall stability of links in the network by providing a more precise measure of the connectivity of the fuzzy graphs. It is particularly significant in situations where connectivity strength and dependability possess a degree of fuzziness, including communication networks with variable signal intensities or transit systems with unpredictable travel durations. In this article, we describe the types of edges in Pythagorean fuzzy graphs and the ideas of the Pythagorean fuzzy trees and cycles. We define the Pythagorean fuzzy average edge connectivity of Pythagorean fuzzy graphs using the concept of minimal Pythagorean fuzzy local edge cut. We provide the bounds for the Pythagorean fuzzy average edge connectivity of Pythagorean fuzzy graphs and strong Pythagorean fuzzy graphs. We discuss the Pythagorean fuzzy average edge connectivity of edge-deleted Pythagorean fuzzy subgraphs of Pythagorean fuzzy graphs. Moreover, we determine the effect of the different types of edges on the Pythagorean fuzzy average edge connectivity. We establish some results on Pythagorean fuzzy average edge connectivity. Furthermore, we design some algorithms to compute the Pythagorean fuzzy average edge connectivity of particular Pythagorean fuzzy graphs as complete Pythagorean fuzzy graphs and saturated Pythagorean fuzzy cycles. We provide the application of Pythagorean fuzzy average edge connectivity in human trafficking. Finally, we compare the suggested approach with an existing model to illustrate its viability and applicability.