Domination Number Based on Fuzzy Bridge And Application

Abstract

The purpose of this paper is to  apply of      novel  notion of fuzzy  dominating sets as $\alpha$-strong dominating set and fuzzy domination number  in   fuzzy graphs  based on  fuzzy bridges.In order to realize the article's goals, we  compute  fuzzy  dominating sets and  fuzzy domination number of wheel fuzzy  graphs. The main  our method, in this  research is  based on computations of fuzzy domination number of wheel fuzzy  graphs  with  distinct fuzzy vertices and to generalize of  computations of fuzzy domination number of wheel fuzzy  graphs  with  any given fuzzy vertices.As a result of the research, is compute of fuzzy  dominating sets and  fuzzy domination number of    complete (multi)partite fuzzy graphs with  distinct fuzzy vertices. Also,  is found some critical fuzzy vertices in  complete (multi)partite fuzzy graphs such that   allow  us to by deleting some edges from   complete (multi)partite fuzzy graphs, obtain the fuzzy  dominating sets and  fuzzy domination number of  wheel fuzzy  graphs and complete partite fuzzy graphs.The paper includes implications for the development of fuzzy graph,  and for modeling  the  uncertainty problems by fuzzy vertices, fuzzy edges and their relations  as fuzzy graph.The new conception of  fuzzy  dominating sets as $\alpha$-strong dominating set and fuzzy domination number  in   wheel fuzzy  graphs and complete (multi)partite fuzzy graphs based on  fuzzy bridges  was given for the first time in this paper. We find an Algorithm that can compute  fuzzy domination number of  wheel fuzzy  graphs and complete (multi)partite fuzzy graphs and can apply fuzzy domination number of  fuzzy graphs in modeling of  real problems of complex networks.