STUDY ON STRONGEST DOMINATING SETS IN FUZZY GRAPHS AND THESE APPLICATIONS IN FUZZY TREES

Zadeh's paper developed a theory which proposed making the grade of membership of an element in a subset of a universal set a value in the closed interval of real numbers. Zadeh's ideas have found applications in many areas of science and technology. Theoretical mathematics have also been touched by fuzzy set theory. The ideas of fuzzy set theory have been introduced into topology, abstract algebra, geometry, graph theory, and analysis. Fuzzy graphs were introduced by Rosenfeld, who has described the fuzzy analogue of several graph theoretic concepts like paths, cycles, trees and connectedness. Nagoor Gani and Chandrasekaran defined dominating set and domination number in fuzzy graphs in. In this paper we study domination in fuzzy graphs. We introduce the concept of strength of strongest dominating set by using membership values of vertices and edges in fuzzy graphs. We present some bounds for the strength of strongest dominating set in fuzzy graphs and then determine the strength of strongest dominating set in some families of fuzzy graphs including complete fuzzy graphs and complete bipartite fuzzy graphs. We also introduce the concept of strength of strongest k-step dominating set in fuzzy graphs, and present various bounds for the strength of strength of strongest ۱-step dominating set in fuzzy graphs.

کلیدواژه ها:

Dominating set ، Exact ۱-step dominating set ، Strongest dominating set in fuzzy graphs ، complement of fuzzy graphs