Abstract: A colored hydrogen- depleted graph was proposed to replace a molecular graph so as to obtain good discrimination of the complex organic compounds by dyeing both the edges and the vertices. Furthermore, the topological index Xu based on the adjacency matrix A and distance matrix D was derived and further adapted to the multiplybonds,heteroatom-containing compounds by using the related ratio of bond length to C-C bond length in place of the adjacent topological distance and the valence δ_i  in place of the degree of vertex v_i. The index was highly correlated with the gas chromatography retention index of alkanes and cyclanes and alcohols and ketones and esters , and promised to be a useful parameter in the QSPR/ QSAR research.

Key words: graph theory, topological indices, organic compounds, gas chromatography retention index, QSPR/QSAR