JSCS Vol 62, No 3
J. Serb. Chem. Soc. 62(3)
Original scientific paper
Wiener index and intermolecular forces
IVAN GUTMAN and J. HERMAN POTGIETER*
Faculty of Science,
University of Kragujevac, P. O. Box 60, YU-34000 Kragujevac, Yugoslavia, and
*Pretoria Portland Cement TSD, P. O. Box 40073, Cleveland, 2022 Johannesburg,
Republic of South Africa
(Received 13 July 1996)
The Wiener indrex (W) is known to be well correlated with a variety of physico-chemical properties of numberous classes of organic compounds. It was suspected for some time that the success of W has its origin in the fact that W represents a measure of intermolecular (attractive) forces, especially in the case of non-polar molecules. We now corroborate this hypothesis by showing that in the case of alkanes W is proportional to the acentric factor as well as to the parameter a in the van der Waals equation.
Key words: Wiener index, acentric factor, intermolecular forces.
Suppression difference in Wiener numbers for acyclic molecular graphs
Department, Joetsu University of Education, Yamayashiki, Joetsu,
Niigata Prefecture 943, Japan
(Received 19 May 1996)
A rule for eliminating all terminal vertices (and all the edges attached to them) in acyclic molecular graphs is defined. Successive use of this operation leads to a sequence (G0,G1,G2...) of acyclic molecular graphs. It is suggested that the difference between Wiener number W(Gk) and W(Gk+1) relates to the difference between T(Gk) and T(Gk+1) where T stands for boiling point or critical temperature.
Key words: Wiener number, successive suppression, difference, physical quantity, acyclic molecular graph.
Decomposition of the Wiener number into contributions coming from homodistant pairs of vertices. Definition and a QSAR application
ERNESTO ESTRADA and LISSETTE RODRIGUEZ
Departamento de Dise¤o de F rmacos, Centro de Bioactivos Quˇmicos, Universidad Central de Las Villas, Santa Clara 54830, Villa Clara, Cuba
(Received 19 July 1996)
The Wiener number is expressed in terms of homodistant pairs of vertices of the molecular graph. Two pairs of vertices are called homodistant if they are separated by the same distance, i.e., if they correspond to equal entries in the distance matrix. The numbers of homodistant pairs of vertices of different order, that is, the counts of ones, twos, threes, etc., in the distance matrix, are shown to differ from the path numbers of graphs of molecules containing cycles. These numbers are used to describe the antiviral activity of benzimidazole derivatives. The model found contains two independent variables: one related to global topological features of molecules, the other related to possible specific interactions with biological receptors. The quantitative structure-activity model found is compared with other models based on molecular connectivity indices, the original Wiener number and the number of paths of different length. The present approach has some strong and weak features, relative to other QSAR studies of specific drug-receptor interactions.
Key words: Wiener topological index, QSAR study, benzimidazole derivatives, antiviral activity.
The relation between the Wiener indices of phenylenes and their hexagonal squeezes
IVAN GUTMAN, SVETLANA MARKOVIC, LJILJANA POPOVIC, ZORA SPALEVIC and LJILJANA PAVLOVIC
Faculty of Science, University of Kragujevac, P. O. Box 60, YU-34000 Kragujevac, Yugoslavia
(Received 31 August 1996)
If PH is a phenylene, HS its hexagonal squeeze and ID the inner dual of HS, then the following relation exists between the respective Wiener indices (W): W(PH) = (9/4)[W(HS) + 16 W(ID) - (2 h + 1) (4 h + 1)]-, where h is the number of hexagons of PH and HS, i.e., the number of vertices of ID. This equality is a new member of the series of recently discovered connections between topological properties of PH and HS.
Key words: Wiener index, phenylenes, hexagonal squeeze.
On applicability of the Wiener index to estimate relative stabilities of the higher-fullerene IPR isomers
ZD-EN<202>-K SLANINA, MIN-CHU CHAO, SHYI-LONG LEE and IVAN GUTMAN*
Chemistry, National Chung-Cheng University Ming-Hsiung, Chia-Yi 62117, Taiwan
*Faculty of Science, University of Kragujevac, P.O. Box 60, YU-34000 Kragujevac, Yugoslavia
(Received 16 August 1996)
The Wiener index is tested as a possible measure of the relative-stability order for the isolated-pentagon-rule (IPR) isomers of higher fullerens. The quotient works very well for the C80 IPR set (and is superior to the topological HOMO-LUMO gap). The Harary index produces a comparable correlation. The Wiener index, however, does not produce a good stability correlation for the IPR sets of C84 and C86
Key words: Wiener index, higher fullerenes, IPR structures, relative stabilities.
Estimation of the inhibition of DNA synthesis by the Wiener index
PADMAKAR V. KHADIKAR, SNEHA KARMARKAR, SHOBHA SHARMA*, ARJUN DAS SEERWANI** and SHOBHA JOSHI**
Faculty of Science,
D.A.V.V., 3 Khatipura, Indore 452001, India;
*Department of Botany, Govt. Girls P.G. College, Moti Tabela, Indore; and
**Department of Chemistry, Holkar Science College, Indore 452001, India
(Received May 28, 1996)
The paper describes topological estimation of the inhibition of DNA synthesis by hydroxyurea(s) using the Wiener index (W). The data suggest that the hydroxyureas inhibit a reaction in the biosynthesis of deoxyribonucleotides, which can be modeled by W. The relationship between W and the inhibitory activity is discussed. The inhibitory potential is also correlated with the increments obtained by decomposition of W into its single and double bond contributions.
Key words: DNA synthesis, inhibition by hydroxyurea, topological estimation, graph theory, hydroxyurea.
of Wiener vis-a-vis Szeged indices in predicting polychlorinated biphenyls in
SNEHA KARMARKAR, SANJAY KARMARKAR*, SHOBHA JOSHI**, ARADHANA DAS*** and PADMAKAR V. KHADIKAR****
Chemistry, Islamia Karimia College, Indore-452001, India;
*Laxmi-Pest Control, Old Palasia, Indore-452001, India;
**Chemistry Department, Government Holkar Science College, Indore-452001, India;
***School of Chemistry, D.A. University, Khandwa Road, Indore-452001, India; and
****Faculty of Sciences, D.A.V.V., 3, Khatipura, Indore-452007, India
(Received 28 May 1996)
The paper gives a brief account of the recently introduced Szeged index (Sz). This index has been calculated for a series of polychlorinated biphenyls and used in predicting their occurrence in the environment. The potential of Sz relative to the Wiener index (W) is critically discussed. The advantage of Sz over W is established by employing regression analysis.
Key words: Szeged index, Wiener index, polychlorinated biphenyls.
A comparative study of the Wiener, Schultz and Szeged indices of cycloalkanes
ARADHANA DAS, GYULA DOMOTOR*, IVAN GUTMAN**, SHOBHA JOSHI***, SNEHA KARMARKAR§, DAYASHANKAR KHADDAR§§, TRIPTI KHADDAR§§, PADMAKAR V. KHADIKAR§§, LJILJANA POPOVIC**, NITIN S. SAPRE, NEELIMA SAPRE§§§ and ANJALI SHIRHATTI**
Chemical Sciences, Vigyan Bhawan, Indore, India,
*Institute of Physical Chemistry, Attila J˘zsef University, P. O. Box 105,
H-6701 Szeged, Hungary,
**Faculty of Science, University of Kragujevac, YU-34000 Kragujevac, Yugoslavia,
***Holkar Science College, Indore, India,
§Islamia Carimia College, Indore, India,
§§Faculty of Science, D. A. V. V., Indore, India, and
§§§ "N. N. Computers", Indore , India
(Received 22 June 1996)
In alkanes, the Wiener (W), Schultz (MTI) and Szeged (Sz) topological indices are known to be closely related, being thus equally capable of predicting the physico-chemical properties of these compounds. We have now examined cycloalkanes and found that for them: (a) W, MTI and Sz are linerly correlated, (b) the correlations of W, MTI and Sz with boiling point, molar volume and molar refraction are curvilinear and for all three indices are of nearly equal quality, and (c) W yields slightly better results than MTI and Sz.
Key words: Wiener index, Szeged index, Schultz index, molecular topological index, cycloalkanes.
Dual descriptors in the calculation of Wiener numbers
MIRCEA V. DIUDEA, CORINA M. POP, GABRIEL KATONA and ANDREY A. DOBRYNIN*
Chemistry, "Babes-Bolyai" University, 3400 Cluj, Romania,
*Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090, Rusia
(Received 16 June 1996)
Wiener, W, and hyper-Wiener, WW, numbers can be calculated on the grounds of two basic matrices: Wiener, W, and distance, D, respectively. The spectral data of seven different matrix descriptors are calculated for the set of octane isomers. The derived numbers are tested for separating and correlating ability.
Key words: Wiener numbers, derived matrices, derived numbers, spectral data, structure - property correlations.
New topological indices for the study of isomeric coumpounds
Silesian Academy of Medicine, Faculty of Pharmacy PL-41-200 Sosnowie, Poland
(Received 19 May 1996)
A new optical topological index (Iopt) and new stereoisomeric topological index (ISTI) are put forward which enable the distanction between isomers of D and L configuration and between stereoisomers with hydroxyl groups in axial and equatorial positions, respectively.
Key words: Optical topological index, stereoisomeric topological index
New topological indices for distinguishing between enantiomers and stereoisomers: A mathematical analysis
IVAN GUTMANa and ALINA PYKA*
Faculty of Science,
University of Kragujevac, YU-34000 Kragujevac, Yugoslavia, and
*Silesian Academy of Medicine of Pharmacy, PL-41200 Sosnowiec, Poland
(Received 20 June 1996)
Two structure-descriptors: the optical topological index (Iopt), distinguishing between enantiomers, and the stereoisomeric topological index (ISTI), distinguishing between stereoisomers, were recently introduced. Both Iopt and ISTI are defined via the distance matrix of the respective molecular graph. We now establish some fundamental properties of Iopt and ISTI and, in particular, show how they are related to the Wiener index.
Key words: optical topological index, stereoisomeric topological index, Wiener index.
Derived Szeged and Cluj Indices
M. V. DIUDEA, B. PARV* and M.I. TOPAN**
Chemistry, "Babes-Bolyai" University, 3400 Cluj,
*Department of Mathematics, "Babes-Bolyai" University, Cluj and
**Departments of Computers, Polytechnic University, Cluj, Romania
(Received 19 May 1996)
Wiener number analogues, Szeged and Cluj are derived in three ways: (i) as reciprocal property; (ii) as distance-extended numbers and (iii) as Schultz-type numbers. The novel numbers are exemplified and tested for correlating ability.
Key words: wiener number analogues, Szeged number analogues, Cluj number analogues, reciprocal property, distance-extended, Schultz number analogues
Transformations of distances into adjacencies
Jurkovi}ova 13, 63800 Brno, The Czech Republic
(Received 14 July 1996)
The code matrix of trees generates their distance matrix, and transforms the incidence matrix of the complete graph into the path matrix. Adjacency and distance matrices of all graphs are related by the transformation of distance moments (dij)k as aij = lim (dij)-k (k ->0) The dependence of the eigenvalues of distance-moment matrices on k is studied on the examples of a 5-vertex linear chain, a 4-membered cycle and a cube. The distance moments can also be changed by different configurations of molecular graphs. The chemical significance of the results obtained in pointed out.
Key words: Adjacency matrix, distance matrix, code matrix, walk matrix, eigenvalues.
Novel vertex-degree-weighted graph invariants
MINATI KUANAR and BIJAY K. MISHRA
Centre of Studies
in Surface Science and Technology, Depatment of Chemistry,
Sambalpur University, Yuiti Vihar 768 019, India
(Received 15 Octobar 1996)
Some vertex-degre-weighted topological indices (TIs) of C3 to C9 alkane isomers are derived by matrix algebraic operation of vertex-degree-matrix on distance and walk matrices. The correlations of these TIs with various physical properties of the corresponding alkanes are compoared with those of some Schultz-type and other topological parameters.
Key words: Vertex-degree-matrix, topological indices, distance matrix, walk matrix, Wiener index, Schutlz-type parameter.