Four new topological indices based on the molecular path code.
J Chem Inf Model
; 47(3): 716-31, 2007.
Article
en En
| MEDLINE
| ID: mdl-17367126
ABSTRACT
The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots (iv) distance-Attenuated index A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots Path-count index P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.
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Colección:
01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Prognostic_studies
Idioma:
En
Revista:
J Chem Inf Model
Asunto de la revista:
INFORMATICA MEDICA
/
QUIMICA
Año:
2007
Tipo del documento:
Article
País de afiliación:
Estados Unidos