Chemical and molecular graphs have fundamental applications in chemoinformatics, quantitative structureproperty
relationships (QSPR), quantitative structure-activity relationships (QSAR), virtual screening of chemical
libraries, and computational drug design. Chemoinformatics applications of graphs include chemical structure
representation and coding, database search and retrieval, and physicochemical property prediction. QSPR, QSAR and
virtual screening are based on the structure-property principle, which states that the physicochemical and biological
properties of chemical compounds can be predicted from their chemical structure. Such structure-property correlations are
usually developed from topological indices and fingerprints computed from the molecular graph and from molecular
descriptors computed from the three-dimensional chemical structure. We present here a selection of the most important
graph descriptors and topological indices, including molecular matrices, graph spectra, spectral moments, graph
polynomials, and vertex topological indices. These graph descriptors are used to define several topological indices based
on molecular connectivity, graph distance, reciprocal distance, distance-degree, distance-valency, spectra, polynomials,
and information theory concepts. The molecular descriptors and topological indices can be developed with a more general
approach, based on molecular graph operators, which define a family of graph indices related by a common formula.
Graph descriptors and topological indices for molecules containing heteroatoms and multiple bonds are computed with
weighting schemes based on atomic properties, such as the atomic number, covalent radius, or electronegativity. The
correlation in QSPR and QSAR models can be improved by optimizing some parameters in the formula of topological
indices, as demonstrated for structural descriptors based on atomic connectivity and graph distance.
Keywords: Quantitative structure-property relationships, QSPR, quantitative structure-activity relationship (QSAR), network-
QSAR, virtual screening of chemical libraries, computational drug design, molecular graph, topological index, graph spectra,
graph polynomial, distance-valency, graph entropy, graph information.
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