The topological index F* is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecule, the structural features of atoms on top and the bonded cases of the adjacent atoms respectively. The standard formation enthalpies of ABn(g) molecules were correlated with F* (A= C, Al, Si, Ti, Zr, B =F, Cl, Br, I, H, n=1-4) and these correlation coefficients are all more than 0.96.Some molecules (e.g CH4, SiH4,etc.)can be preferably handled by F* but can not be dealt with by other topological indices.By contrast to traditional hydrogen suppressed graph,the contribution of hydrogen atoms to structures and properties of molecules is considered.