Domination Number Based on Fuzzy Bridges in Fuzzy Graphs and Applications
Mohammad Hamidi, Mohammad Esmaiel Nikfar · Research Square · 2022
Abstract In this paper, we consider the notion of (crisp)domination set of fuzzy graphs via fuzzy bridges and compute domination numbers in this regard. Indeed it is tried to combine the fuzzy values of both vertices and edges to present this domination number in fuzzy graphs. The main method in this research is based on the computation of domination number of complete fuzzy graphs with vertices depend on the distinct fuzzy value and generalization of domination number of complete fuzzy graphs with vertices depending on the indistinct fuzzy value. As a result of this study is to compute of domination number of cyclic strong fuzzy graphs with vertices depending on the distinct fuzzy value. Also, it is analyzed some critical vertices in cyclic strong fuzzy graphs such that by linking some edges in these vertices to cyclic strong fuzzy graphs, the domination number of complete fuzzy graphs is obtained. Thus there is a relationship between the domination number of cyclic strong fuzzy graphs and the domination number of complete fuzzy graphs by removing some special edges in complete fuzzy graphs. The paper includes implications for the development of fuzzy graphs, and for modeling the uncertainty problems by domination numbers and applications in some complex networks. The new conception of domination number in fuzzy graphs based on fuzzy bridges was given for the first time in this paper. We find an Algorithm that can compute the domination number of complete and cyclic strong fuzzy graphs and can apply it in the modeling of real problems of complex networks.