Domination Number Based on Fuzzy Bridge And Application

This paper considers the notion of α-strong dominating set based on fuzzy bridges in fuzzy graphs and computes the domination number of wheel fuzzy graphs and complete (multi) partite fuzzy graphs. In this regard, we consider the fuzzy cycles and compute the domination number of wheel fuzzy graphs, supremum center-based wheel fuzzy graph, infimum center-based wheel fuzzy graph, and complete (multi) partite fuzzy graphs with any given fuzzy vertices. It investigated the relationship between the domination number of wheel fuzzy graphs and complete (multi) partite fuzzy graphs via some critical fuzzy vertices in these classes of fuzzy graphs. The new conception of domination number of wheel fuzzy graphs and complete (multi)partite fuzzy graphs based on fuzzy bridges, was given for the first time in this paper and we found an Algorithm in this regard. In the final, we apply the domination number of fuzzy graphs in modeling of real problems of complex networks.