2014
5
2
2
76
The eccentric connectivity index of bucket recursive trees
2
2
If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.
1

77
83


Ramin
Kazemi
Imam Khomeini international university
Imam Khomeini international university
Iran
r.kazemi@sci.ikiu.ac.ir
Bucket recursive trees
eccentric connectivity index
Convergence in probability
Asymptotic normality
Altan derivatives of a graph
2
2
Altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. We now provide a generalization of the altan concept, applicable to any graph. Several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. Among these are results pertaining to Kekulé structures/perfect matchings, determinant of the adjacency matrix, and graph spectrum.
1

85
90


Ivan
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac,
Serbia
gutman@kg.ac.rs
Altan graph
Molecular Graph
Kekulé structure
perfect matching
Spectrum (of graph)
Upper and lower bounds of symmetric division deg index
2
2
Symmetric Division Deg index is one of the 148 discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. Symmetric Division Deg index is defined by $$ SDD(G) = sumE left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right), $$ where $d_i$ is the degree of vertex $i$ in graph $G$. In this paper we provide lower and upper bounds of SDD index in some classes of graphs and determine the corresponding extremal graphs.
1

91
98


Alexander
Vasilyev
University of Primorska, IAM
University of Primorska, IAM
Slovenia
alexander.vasilyev@upr.si
Symmetric division deg index
Adriatic index
Polygonal tiling of some surfaces containing fullerene molecules
2
2
A tiling of a surface is a decomposition of the surface into pieces, i.e. tiles, which cover it without gaps or overlaps. In this paper some special polygonal tiling of sphere, ellipsoid, cylinder, and torus as the most abundant shapes of fullerenes are investigated.
1

99
105


Ali Asghar
Rezaei
University of Kashan
University of Kashan
Iran
a_rezaei@kashanu.ac.ir
Euler characteristic
Fullerene
Polygonal tiling
On the reliability wiener number
2
2
One of the generalizations of the Wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. The Reliability Wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. Closed expressions are derived for the Reliability Wiener number of paths, cycles, stars and brooms. It is shown that the Reliability Wiener number can be used as a measure of branching.
1

107
118


Darja
Rupnik Poklukar
University of Ljubljana
University of Ljubljana
Slovenia
darja.rupnikpoklukar@fs.unilj.si


Janez
Zerovnik
University of Ljubljana
University of Ljubljana
Slovenia
janez.zerovnik@fs.unilj.si
Reliability Wiener number
Edge probability
Branching
Estimation of pigment magnitudes in synthetic leather by using scanner and artificial neural network
2
2
In the present work the magnitudes of pigments in the synthetic leather, were measured by means of scanner. Initially synthetic leather samples pigmented by three different pigments of yellow, blue and red colors were prepared. Then the pigmented samples were scanned, and the values of RGB of images were calculated. The artificial neural network (ANN) method used to make relation between RGB values and pigment magnitudes. The method was successfully applied for the estimation of pigment magnitudes in the synthetic leather samples.
1

119
125


Peyman
Valipour
Islamic Azad University of Ghaemshahr branch
Islamic Azad University of Ghaemshahr branch
Iran
drpeiman.valipour@yahoo.com


Mansour
Mafi
Islamic Azad University of Kashan branch
Islamic Azad University of Kashan branch
Iran
mansour.mafi@gmail.com


Mahshid
Faridi
Islamic Azad University of Kashan branch
Islamic Azad University of Kashan branch
Iran
mahsid.faridi2@gmail.com
Synthetic leather
pigment
Determination
Scanner
Artificial Neural Network
Prediction of the adsorption capability onto activated carbon of liquid aliphatic alcohols using molecular fragments method
2
2
Quantitative structureproperty relationship (QSPR) for estimating the adsorption of aliphatic alcohols onto activated carbon were developed using substructural molecular fragments (SMF) method. The adsorption capacity of activated carbon (gr/100grC) for 150 aliphatic alcohols onto activated carbon (AC) is studied under equilibrium conditions. Forward and backwards stepwise regression variable selection and multilinear regression (MLR) are combined to describe the effect of molecular structure on the adsorption capacity of activated carbon according to the QSPR method. To quantitatively relate adsorption capacity (Qe) with the molecular structure MLR analysis is performed on the set of 15 substructural molecular fragments (SMF) provided by the software ISIDA. The five fragments selected by variable subset selection, all belonging to the subfragments, adequately represent the structural factors influencing the affinity of alcohols to AC in the adsorption process. Finally, a QSPR model is selected based on leaveoneout crossvalidation and its prediction ability is further tested on 30 representative compounds excluded from model calibration. The prediction results from the MLR models are in good agreement with the experimental values. By applying MLR method we can predict the test set (30 compounds) with squared cross validated correlation coefficient (Q2ext) of 0.9538 and root mean square error (RMSE) of 2.0832.
1

127
142


Saadi
Saaidpour
Saadi Saaidpour, PhD
Assistant Professor of Analytical Chemistry
Chemistry Department,Faculty of Science
Sanandaj Branch, Islamic Azad University
Sanandaj, Iran
Saadi Saaidpour, PhD
Assistant Professor
Iran
saadisaaidpour@gmail.com
Activated carbon
Adsorption
Aliphatic alcohols
QSPR
SMF method
A note on the zerothorder general randić index of cacti and polyomino chains
2
2
The present note is devoted to establish some extremal results for the zerothorder general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.
1

143
152


Akbar
Ali
National University of Computer and Emerging Sciences, LahorePakistan
National University of Computer and Emerging
Pakistan
akbarali.maths@gmail.com


Akhlaq
Bhatti
National University of Computer and
Emerging Sciences, Lahore, Pakistan
National University of Computer and
Emerging
Pakistan
akhlaq.ahmad@nu.edu.pk


Zahid
Raza
National University of Computer and
Emerging Sciences, Lahore, Pakistan
National University of Computer and
Emerging
Pakistan
zahid.raza@nu.edu.pk
topological index
Zerothorder general Randi'{c} index
Polyomino chain
Cacti