Strong inverse domination in fuzzy graphs
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The concept of domination in graph theory has been widely studied due to its applications in network theory, social sciences, and optimization problems. In recent years, this concept has been extended to fuzzy graphs, where uncertainty and partial membership are incorporated into the structure of vertices and edges. In this paper, the inverse domination in fuzzy graphs using strong arcs is introduced. The strong inverse domination number of classes of fuzzy graphs, such as complete fuzzy graphs, complete bipartite fuzzy graphs, and fuzzy cycles, is determined. A relation is established between the strong inverse domination number and the strong independence number. Finally, the practical importance of the new concept of inverse domination in fuzzy graphs is nicely presented through a real-life example.
Abstract
The concept of domination in graph theory has been widely studied due to its applications in network theory, social sciences, and optimization problems. In recent years, this concept has been extended to fuzzy graphs, where uncertainty and partial membership are incorporated into the structure of vertices and edges. In this paper, the inverse domination in fuzzy graphs using strong arcs is introduced. The strong inverse domination number of classes of fuzzy graphs, such as complete fuzzy graphs, complete bipartite fuzzy graphs, and fuzzy cycles, is determined. A relation is established between the strong inverse domination number and the strong independence number. Finally, the practical importance of the new concept of inverse domination in fuzzy graphs is nicely presented through a real-life example.