Abstract
In theoretical medicine, topological indices are defined to test the medicine and pharmacy characteristics, such as melting point, boiling point, toxicity and other biological activities. As basic molecular structures, hexagonal jagged-rectangle and distance-regular structure are widely appeared in medicine, pharmacy and biology engineering. In this paper, we study the chemical properties of hexagonal jagged-rectangle from the mathematical point of view. Several vertex distance-based indices are determined. Furthermore, the Wiener related indices of distance-regular structure are also considered.