University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
The eccentric connectivity index of bucket recursive trees
77
83
EN
Ramin
Kazemi
Imam Khomeini international university
r.kazemi@sci.ikiu.ac.ir
10.22052/ijmc.2014.5671
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.
Bucket recursive trees,Eccentric connectivity index,Convergence in probability,Asymptotic normality
http://ijmc.kashanu.ac.ir/article_5671.html
http://ijmc.kashanu.ac.ir/article_5671_c75e8f8a191feb37be45cb549d22b33b.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
Altan derivatives of a graph
85
90
EN
Ivan
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
gutman@kg.ac.rs
10.22052/ijmc.2014.6127
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.
Altan graph,Molecular graph,Kekulé structure,Perfect Matching,Spectrum (of graph)
http://ijmc.kashanu.ac.ir/article_6127.html
http://ijmc.kashanu.ac.ir/article_6127_acb31ccf5c46d78d329317d13a401cc2.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
Upper and lower bounds of symmetric division deg index
91
98
EN
Alexander
Vasilyev
University of Primorska, IAM
alexander.vasilyev@upr.si
10.22052/ijmc.2014.7357
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.
Symmetric division deg index,Adriatic index
http://ijmc.kashanu.ac.ir/article_7357.html
http://ijmc.kashanu.ac.ir/article_7357_78bfab656717a8a35de2906a6ca46a99.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
Polygonal tiling of some surfaces containing fullerene molecules
99
105
EN
Ali Asghar
Rezaei
University of Kashan
a_rezaei@kashanu.ac.ir
10.22052/ijmc.2014.7375
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.
Euler characteristic,Fullerene,Polygonal tiling
http://ijmc.kashanu.ac.ir/article_7375.html
http://ijmc.kashanu.ac.ir/article_7375_490966fb9747f786985dfc15d4bc6a1a.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
On the reliability wiener number
107
118
EN
Darja
Rupnik Poklukar
University of Ljubljana
darja.rupnik-poklukar@fs.uni-lj.si
Janez
Zerovnik
University of Ljubljana
janez.zerovnik@fs.uni-lj.si
10.22052/ijmc.2014.7377
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.
Reliability Wiener number,Edge probability,Branching
http://ijmc.kashanu.ac.ir/article_7377.html
http://ijmc.kashanu.ac.ir/article_7377_5ee148bffddfb55795e543f75ea1b00d.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
Estimation of pigment magnitudes in synthetic leather by using scanner and artificial neural network
119
125
EN
Peyman
Valipour
Islamic Azad University of Ghaemshahr branch
drpeiman.valipour@yahoo.com
Mansour
Mafi
Islamic Azad University of Kashan branch
mansour.mafi@gmail.com
Mahshid
Faridi
Islamic Azad University of Kashan branch
mahsid.faridi2@gmail.com
10.22052/ijmc.2014.7592
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.
Synthetic leather,Pigment,Determination,Scanner,Artificial Neural Network
http://ijmc.kashanu.ac.ir/article_7592.html
http://ijmc.kashanu.ac.ir/article_7592_3894358a7efd1daea46abaa29a027d2f.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
Prediction of the adsorption capability onto activated carbon of liquid aliphatic alcohols using molecular fragments method
127
142
EN
Saadi
Saaidpour
Saadi Saaidpour, PhD
Assistant Professor of Analytical Chemistry
Chemistry Department,Faculty of Science
Sanandaj Branch, Islamic Azad University
Sanandaj, Iran
saadisaaidpour@gmail.com
10.22052/ijmc.2014.7608
Quantitative structure-property 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 leave-one-out cross-validation 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.
Activated Carbon,Adsorption,Aliphatic alcohols,QSPR,SMF method
http://ijmc.kashanu.ac.ir/article_7608.html
http://ijmc.kashanu.ac.ir/article_7608_457efe7ba6c1f3fa53a5e5327016487a.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
5
2
2014
11
01
A note on the zeroth-order general randić index of cacti and polyomino chains
143
152
EN
Akbar
Ali
National University of Computer and Emerging Sciences, Lahore-Pakistan
akbarali.maths@gmail.com
Akhlaq
Ahmad
Bhatti
National University of Computer and
Emerging Sciences, Lahore, Pakistan
akhlaq.ahmad@nu.edu.pk
Zahid
Raza
National University of Computer and
Emerging Sciences, Lahore, Pakistan
zahid.raza@nu.edu.pk
10.22052/ijmc.2014.7611
The present note is devoted to establish some extremal results for the zeroth-order 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.
Topological index,Zeroth-order general Randi'{c} index,Polyomino chain,Cacti
http://ijmc.kashanu.ac.ir/article_7611.html
http://ijmc.kashanu.ac.ir/article_7611_7ff25b2af07cf37198531204336ebb06.pdf