J. Galvez et al., Indices of differences of path lengths: Novel topological descriptors derived from electronic interferences in graphs, J COMPUT A, 14(7), 2000, pp. 679-687
Novel topological descriptors, namely indices of differences of path length
s (DPs), are deduced from the physical model of wave interferences. Two ele
ctrons, moving through a circuit graph within a diffraction experiment, int
erfere in a given vertex of the graph. It is demonstrated that the overall
sum of the inverse of the squares of the differences of topological distanc
es between all pairs of vertices of the graph is a measure of the mean glob
al kinetic energy of the electrons which are able to produce a constructive
interference. New topological indices, namely indices of differences of pa
th lengths are thus introduced as derived from such a diffraction pattern.
These indices, according to the above expressed, should be a measure of the
electron mobility within the molecule. As a consequence, a good prediction
is to be expected for properties related to such mobility, such as resonan
ce energy in aromatic hydrocarbons. Our results confirm that in fact, the r
esonance energies are well predicted by this means. Moreover, the new indic
es demonstrate to be very useful in the evaluation of biological properties
such as antibacterial activities of a wide set of heterogeneous compounds.