Vertex Reducible Total Labeling Algorithm for Random Graphs

With the rise of practical networks such as social networks, biological networks, and information networks, graph theory has made significant progress in studying these complex network structures. This article proposes a new concept of vertex reducible total labeling based on existing icon labeling concepts and practical problems, and designs a Vertex reducible total labeling algorithm. This algorithm adopts an iterative optimization approach to solve all non isomorphic graph sets within a finite point, obtaining the results of the path graph, circle graph, star graph, and the joint graph formed by the combination of these special graphs within a finite point. Through experimental results analysis, several joint graph theorems are summarized and proved.