Difference Square Mean Fuzzy Labelling of Graphs Constructed from Path Graph

Abstract

Computer science applications make extensive use of graph theory. Information mining, picture classification, grouping images, photo capture, and connectivity are particularly important study areas in computer science. Fuzzy labelling models provide better accuracy, adaptability, and interoperability to the framework than conventional fuzzy models. They are used in many areas of basic mathematics, including traditional computer science and physical scientific study. A common problem in mathematics is the distance properties in a graph. In fuzzy mean labelling graphs, paths have some exciting applications. Using lengths to securely identify the vertex in an organization is one such application. As the outcome, in this study, we explore four paths that are DSMFLs in graphs: comb graph, double comb, path-attached pendant vertex, and path-attached two pendant vertices. In fuzzy labelling graphs, there exist several DSMFLs. Whenever the force of connection between each pair of vertices G matches the value of the membership of the edges, G appears self-sufficient in relation to the DSMF. Furthermore, it is established that any interconnected fuzzy labelling graph is both a path graph and a comb graph.