A Topological Index Based on Distances of Edges of Molecular Graphs

A novel molecular topological index MTI(E) is proposed, based on edge-distances in molecular graphs. Edge-distances in a graph are equal to distances between vertices of the respective line graph. A simple relation is found between edge-distances and the distances between the vertices that are incident to the respective edges. MTI(E) is defined in analogy to the graph theoretical invariant of Schultz (Schultz, H. P. J. Chem. Inf. Comput. Sci. 1989, 29, 227−228). It has integer values and is easy to compute. MTI(E) is found to be well correlated with the heats of formation of alkanes.

[1]  Michael F. Delaney,et al.  Optimization of a similarity metric for library searching of highly compressed vapor-phase infrared spectra , 1985, J. Chem. Inf. Comput. Sci..

[2]  Dejan Plavšić,et al.  Molecular topological index: a relation with the Wiener index , 1992, J. Chem. Inf. Comput. Sci..

[3]  J. Chien.  Raman spectra of aqueous solutions of potassium thiocyanate. , 1947, Journal of the American Chemical Society.

[4]  Fernando Bernardi,et al.  Importance of nonbonded attraction in the stereochemistry of the SN2' reaction , 1975 .

[5]  Marko Razinger,et al.  Structural selectivity of topological indexes in alkane series , 1985, J. Chem. Inf. Comput. Sci..

[6]  G. Leroy,et al.  Graph theory, electronic structures and reaction mechanisms , 1984 .

[7]  Sonja Nikolic,et al.  Comparative study of molecular descriptors derived from the distance matrix , 1992, J. Chem. Inf. Comput. Sci..

[8]  Dejan Plavšić,et al.  The distance matrix in chemistry , 1992 .

[9]  Milan Randić,et al.  Generalized molecular descriptors , 1991 .

[10]  Manuel Garbalena,et al.  Optimum graph-theoretical models for enthalpic properties of alkanes , 1992, J. Chem. Inf. Comput. Sci..

[11]  C.-S. Ai,et al.  Extraction of chemical reaction information from primary journal text , 1990, J. Chem. Inf. Comput. Sci..

[12]  Guenter Bergerhoff,et al.  Chemical Abstracts ONLINE: a study of the quality of controlled terms , 1991, J. Chem. Inf. Comput. Sci..

[13]  M. Randic.  Characterization of molecular branching , 1975 .

[14]  Zlatko Mihalić,et al.  A graph-theoretical approach to structure-property relationships , 1992 .

[15]  Harry P. Schultz,et al.  Topological organic chemistry. 1. Graph theory and topological indices of alkanes , 1989, J. Chem. Inf. Comput. Sci..

[16]  Harry P. Schultz,et al.  Topological organic chemistry. 3. Graph theory, binary and decimal adjacency matrices, and topological indices of alkanes , 1991, J. Chem. Inf. Comput. Sci..