The inverse problems for some topological indices in combinatorial chemistry.

In the original paper, Goldman et al. (2000) launched the study of the inverse problems in combinatorial chemistry, which is closely related to the design of combinatorial libraries for drug discovery. Following their ideas, we investigate four other topological indices, i.e., the sigma-index, the c-index, the Z-index, and the M(1)-index, with a special emphasis on the sigma-index. Like the Wiener index, these four indices are very popular in combinatorial chemistry and reflect many chemical and physical properties. We give algorithmic and analytical solutions for the inverse problems of the four indices. We also show that the SUBTREEVALUE reconstruction problem for the sigma-index is NP-hard.