A new isomorphism determination method of chemical polymers using distance topological matrix

Abstract Compound structure retrieval has become a widely used tool in computer aided drug design, drug identification and chemical database. However, it has historically been a concern of scholars to distinguish the isomers of chemical molecules accurately and quickly, due to the isomorphism of their structure. In this paper, a new shortest distance topological index method (SDTI) is proposed to determine whether chemical molecules are isomorphic or not. Firstly, a bond length adjacency matrix was built to describe the structure diagram of chemical molecules, according to the chemical bonds in the molecular structure, which can accurately describe the adjacency relationship between different atoms. Secondly, the corresponding value is given as the weight of the atom in the chemical molecules for different atoms, and this value is called the valence. The weight of each atom is integrated to construct a one-dimensional atomic weight group, and use this one-dimensional atomic weight group to represent the characteristic information of each atom in the molecule. Then, a numerical value is also given to represent the characteristic connection between any two atoms, and the atomic weight matrix is constructed based on this numerical value. Next, the distance between atoms was determined to construct the weight matrix according to the bond length adjacency matrix and the atomic weight matrix. Then, the shortest distance matrix describing the distance between two atoms was obtained by constantly updating the matrix. The shortest distance topological index was obtained by summing all elements of the distance matrix, which is used to identify the isomorphism of chemical molecules. Finally, a large number of cases have certified that this method is effective, reliable and practical.