Abstract
Graph structures are an essential tool for solving combinatorial problems in computer science and computational intelligence. With an emphasis on signed graphs, picture-fuzzy graphs, and graphs with colored or labeled edges, this study explores the properties of picture-fuzzy graph topologies. Within these frameworks, it presents key ideas such as the lexicographic-max product, vertex degree, and total degree. The use of picture-fuzzy graphs' lexicographic-max product to tackle intricate problems like human trafficking is a key component of this study. The study illustrates how this strategy can improve decision-making processes in such crucial areas by utilizing the special qualities of picture-fuzzy graphs. The study is supported by informative numerical examples that show how useful these ideas are in real-world situations. In addition, the study offers a thorough algorithmic foundation for applying the lexicographic-max product in practical situations, especially those involving human trafficking. The goal of this framework is to provide a workable approach for applying picture-fuzzy graph structures to enhance decision-making and tackle important societal issues.
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