**JSCS Vol 62, No 3**

J. Serb. Chem. Soc. 62(3)
185-192 (1997)

UDC 661.71:513.83:539.194/.196

JSCS-2171

*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.*

J. Serb.
Chem. Soc. 62(3) 193-197 (1997)

UDC 547.2.084:513.83:539.196

JSCS-2172

*Original scientific paper*

Suppression
difference in Wiener numbers for acyclic molecular graphs

TETSUO MORIKAWA

**Chemistry
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 *(G _{0},G_{1},G_{2}...)* of
acyclic molecular graphs. It is suggested that the difference between Wiener
number

Key words: *Wiener number, successive suppression,
difference, physical quantity, acyclic molecular graph.*

J. Serb.
Chem. Soc. 62(3) 199-205( 1997)

UDC 539.193/.2:513.83-084

JSCS-2173

*Original scientific paper*

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.*

J. Serb.
Chem. Soc. 62(3) 207-210( 1997)

UDC 547.526/.53:513.83

JSCS-2174

*Original scientific paper*

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.*

J. Serb.
Chem. Soc. 62(3) 211-217 (1997)

UDC 513.83-:547.52/.59

JSCS-2175

*Original scientific paper*

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*

**Department of
Chemistry, National Chung-Cheng University Ming-Hsiung, Chia-Yi 62117, Taiwan
and**

***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 C* _{80}* 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 C

Key words: *Wiener index, higher fullerenes, IPR
structures, relative stabilities.*

J. Serb.
Chem. Soc. 62(3) 219-226 (1997)

UDC 547.963.32:542.91/.97

JSCS-2176

*Original scientific paper*

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. *

J. Serb.
Chem. Soc. 62(3) 227-234 (1997)

UDC 547.626:547.539.2:631.42

JSCS-2177

*Original scientific paper*

Novel application
of Wiener vis-a-vis Szeged indices in predicting polychlorinated biphenyls in
the environment

SNEHA KARMARKAR, SANJAY KARMARKAR*, SHOBHA JOSHI**, ARADHANA DAS*** and
PADMAKAR V. KHADIKAR****

**Department of
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.*

J. Serb.
Chem. Soc. 62(3) 235-239 (1997)

UDC 547.21:547.5:513.8

JSCS-2178

*Original scientific paper*

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**

**Institute of
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.

J. Serb.
Chem. Soc. 62(3) 241-250 (1997)

UDC 513.82:513.86/.87;547.217.2/541.621/

JSCS-2179

*Original scientific paper*

Dual descriptors in
the calculation of Wiener numbers

MIRCEA V. DIUDEA,
CORINA M. POP, GABRIEL KATONA and ANDREY A. DOBRYNIN*

**Department of
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.*

J. Serb.
Chem. Soc. 62(3) 251-269 (1997)

UDC 513.82/.86/.87:541.621

JSCS-2180

*Original scientific paper*

New topological
indices for the study of isomeric coumpounds

ALINA PYKA

**Silesian Academy of
Medicine, Faculty of Pharmacy PL-41-200 Sosnowie, Poland**

*(Received 19 May 1996)*

A new optical topological index (*I _{opt}*) and new stereoisomeric
topological index (

Key words: *Optical topological index,
stereoisomeric topological index*

J. Serb.
Chem. Soc. 62(3) 261-265 (1997)

UDC 513.82-84:541.632

JSCS-2181

*Original scientific paper*

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 *(I _{opt})*,
distinguishing between enantiomers, and the stereoisomeric topological index

Key words: *optical topological index,
stereoisomeric topological index, Wiener index.*

J. Serb.
Chem. Soc. 62(3) 267-276 (1997)

UDC 547.21:536.77

JSCS-2182

*Original scientific paper*

Derived Szeged and
Cluj Indices

M. V. DIUDEA, B.
PARV* and M.I. TOPAN**

**Department of
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*

J. Serb.
Chem. Soc. 62(3) 277-287 (1997)

UDC 513.82-84;513.75

JSCS-2183

*Original scientific paper*

Transformations of
distances into adjacencies

MILAN KUNZ

**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 *(d _{ij})^{k}* as

Key words: *Adjacency matrix, distance matrix,
code matrix, walk matrix, eigenvalues.*

J. Serb.
Chem. Soc. 62(3) 289-294 (1997)

UDC 513.82-84:547.21.002.61

JSCS-2184

*Original scientific paper*

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 C_{3} to C_{9}
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.*