Research on Similarity between Generalized Molecular Graphs

The similarity between molecular structures is a meaningful project. The periodic table of elements proposed by D. Mendeleev is based on the similarity of chemical elements. Based on graph theory and computer science, this paper studied the similarity of a kind of connected undirected graph that the vertices may have the same names. Proposed the concept of generalized molecular graphs and their computer representation. Defined and studied six kinds of similarities: identity relations, neighbor identity, isomorphism, degree isomorphism, vertex similarity and edge similarity. The concepts of generalized molecular graphs and the similarity between them can be applied in the field of computer network, nano-materials and the design of drug molecules.