Extension of the <b><i>Z</i></b> Matrix to Cycle-Containing and Edge-Weighted Molecular Graphs

Plavšić, Dejan; Šoškić, Milan; Đaković, Zorislav; Gutman, Iván; Graovac, Ante

doi:10.1021/ci960159o

Cited by 7 publications

(4 citation statements)

References 29 publications

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“…Plavsic ´et al devoted a study to the monocycloalkanes of up to six carbon atoms, using an index Z* derived from the Z matrix. 11 Das et al found for a sample of monocycloalkanes nonlinear correlations of the bps with the Wiener, Schultz, and Szeged indices and a high linear interrelation among these indices. 12 Diudea regressed the bps of some monocycloalkanes against indices derived from the Wiener, Szeged, and Cluj matrices as well as from the corresponding reciprocal matrices.…”

Section: Introductionmentioning

confidence: 96%

“…Even far later others included in their alkane-centered investigations some cycloalkanes, such as Lukovits and Zinn. , Lukovits, Trinajstić, and ourselves studied the detour index, a TI recently introduced especially for cyclic compounds, and its correlation with bps for mixed samples of cyclic and acyclic compounds. Plavsić et al devoted a study to the monocycloalkanes of up to six carbon atoms, using an index Z * derived from the Z matrix . Das et al found for a sample of monocycloalkanes nonlinear correlations of the bps with the Wiener, Schultz, and Szeged indices and a high linear interrelation among these indices .…”

Section: Introductionmentioning

confidence: 99%

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On Topological Indices, Boiling Points, and Cycloalkanes

Rücker

1999

J. Chem. Inf. Comput. Sci.

223

184

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The experimental boiling points (bp) of saturated hydrocarbons (acyclic through polycyclic) up to decanes are systematically compiled. The bp values are classified into groups of lower or higher reliability according to the accuracy and frequency with which they were reproduced by independent researchers. For each hydrocarbon structure the values of several simple topological indices (TI) of widely varying origin are given, including the values of molecular walk counts of various lengths and their sum. The sensitivity of the TIs for structural changes within comprehensive groups of cyclic saturated hydrocarbons is evaluated, and the total walk count is found to be most sensitive. By multilinear regression structure-bp correlations are obtained for various comprehensive compound samples. Both the detour index and the walk counts are found to play a major role in the best models. Comparison of the bp models obtained with those from the recent literature reveals significant improvements for both cyclic and acyclic alkanes, which is attributed in part to the higher quality of experimental data, in part to the use of novel descriptors, and in part to the use of a more diverse pool of descriptors to select from. Despite this a descriptor combination allowing to accurately model cycloalkane bps is not yet found.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

On Topological Indices, Boiling Points, and Cycloalkanes

Rücker

1999

J. Chem. Inf. Comput. Sci.

223

184

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“…Boiling Points of 20 Cycloalkanes. Plavšić et al reported last year (1997) in this journal a structure−boiling point model for 20 cycloalkanes using the Z index of Hosoya and the vertex-connectivity index. The relevant statistical data for a model based on the connectivity index were R = 0.992 and S = 3.70 °C.…”

Section: Resultsmentioning

confidence: 99%

The Vertex-Connectivity Index Revisited

Amić¹,

Bešlo²,

Lučić³

et al. 1998

J. Chem. Inf. Comput. Sci.

237

114

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We report a search for optimum molecular descriptors based on the connectivity index. A suggestion made by several authors that the exponent -0.5 used in the standard formula for computing the connectivity index may not be the optimum for modeling some molecular properties was reexamined. We considered several molecular properties and found that in most cases the optimum value of the exponent is indeed different from -0.5. We suggest that a modified version of the (valence) vertex-connectivity index should be routinely employed in the structure-property modeling instead of the standard version of the index.

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“…For a different looking definition in the 3 dimensional case, see [70]. A different use of the term Z-matrix is in [75]. It may be that some of the conditions in the above definition can be omitted without changing the concept; we have not attempted a minimal axiomatization of Z-matrices.…”

Section: Z-matricesmentioning

confidence: 99%

Polyspherical Coordinate Systems on Orbit Spaces with Applications to Biomolecular Shape

Dix

2006

Acta Appl Math

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Abstract. A general theory of molecular internal coordinates of valence type is presented based on the concept of a Z-system. The Z-system can be considered as a discrete mathematical generalization of the Z-matrix (a molecular geometry file format familiar to chemists) which avoids the principal disadvantage of Z-matrices. Z-matrices are usually only employed for small molecules because there is no easy way to glue two Z-matrices together to get the Zmatrix of a larger molecule. It is shown that Z-matrices are simply Z-systems together with additional extraneous structures and that the Z-systems for any two molecules can be naturally glued together to obtain a Z-system for the combined molecule. A general mathematical framework suitable for the detailed study of molecular geometry is introduced and applied to five and sixmembered molecular rings. A classification of shapes of hexagons with opposite sides and angles congruent is given with explicit parameterizations of the flexible and rigid solutions. The entire mathematical formalism generalizes to a theory of polyspherical coordinate systems on orbit spaces of the group of n-dimensional rigid motions acting on finite collections of points in n-dimensional Euclidean space. The n-dimensional Z-system is a new discrete structure related to abstract simplicial complexes, graded posets, and iterated line graphs. Complete proofs of all the n-dimensional results are given, and connections to other areas of mathematics are noted.

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Extension of the Z Matrix to Cycle-Containing and Edge-Weighted Molecular Graphs

Cited by 7 publications

References 29 publications

On Topological Indices, Boiling Points, and Cycloalkanes

On Topological Indices, Boiling Points, and Cycloalkanes

The Vertex-Connectivity Index Revisited

Polyspherical Coordinate Systems on Orbit Spaces with Applications to Biomolecular Shape

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