eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
77
83
10.22052/ijmc.2014.5671
5671
The eccentric connectivity index of bucket recursive trees
Ramin Kazemi
r.kazemi@sci.ikiu.ac.ir
1
Imam Khomeini international university
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.
https://ijmc.kashanu.ac.ir/article_5671_c75e8f8a191feb37be45cb549d22b33b.pdf
Bucket recursive trees
eccentric connectivity index
Convergence in probability
Asymptotic normality
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
85
90
10.22052/ijmc.2014.6127
6127
Altan derivatives of a graph
Ivan Gutman
gutman@kg.ac.rs
1
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
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.
https://ijmc.kashanu.ac.ir/article_6127_acb31ccf5c46d78d329317d13a401cc2.pdf
Altan graph
Molecular Graph
Kekulé structure
perfect matching
Spectrum (of graph)
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
91
98
10.22052/ijmc.2014.7357
7357
Upper and lower bounds of symmetric division deg index
Alexander Vasilyev
alexander.vasilyev@upr.si
1
University of Primorska, IAM
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.
https://ijmc.kashanu.ac.ir/article_7357_78bfab656717a8a35de2906a6ca46a99.pdf
Symmetric division deg index
Adriatic index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
99
105
10.22052/ijmc.2014.7375
7375
Polygonal tiling of some surfaces containing fullerene molecules
Ali Asghar Rezaei
a_rezaei@kashanu.ac.ir
1
University of Kashan
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.
https://ijmc.kashanu.ac.ir/article_7375_490966fb9747f786985dfc15d4bc6a1a.pdf
Euler characteristic
Fullerene
Polygonal tiling
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
107
118
10.22052/ijmc.2014.7377
7377
On the reliability wiener number
Darja Rupnik Poklukar
darja.rupnik-poklukar@fs.uni-lj.si
1
Janez Zerovnik
janez.zerovnik@fs.uni-lj.si
2
University of Ljubljana
University of Ljubljana
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.
https://ijmc.kashanu.ac.ir/article_7377_5ee148bffddfb55795e543f75ea1b00d.pdf
Reliability Wiener number
Edge probability
Branching
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
119
125
10.22052/ijmc.2014.7592
7592
Estimation of pigment magnitudes in synthetic leather by using scanner and artificial neural network
Peyman Valipour
drpeiman.valipour@yahoo.com
1
Mansour Mafi
mansour.mafi@gmail.com
2
Mahshid Faridi
mahsid.faridi2@gmail.com
3
Islamic Azad University of Ghaemshahr branch
Islamic Azad University of Kashan branch
Islamic Azad University of Kashan branch
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.
https://ijmc.kashanu.ac.ir/article_7592_3894358a7efd1daea46abaa29a027d2f.pdf
Synthetic leather
pigment
Determination
Scanner
Artificial Neural Network
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
127
142
10.22052/ijmc.2014.7608
7608
Prediction of the adsorption capability onto activated carbon of liquid aliphatic alcohols using molecular fragments method
Saadi Saaidpour
saadisaaidpour@gmail.com
1
Saadi Saaidpour, PhD
Assistant Professor of Analytical Chemistry
Chemistry Department,Faculty of Science
Sanandaj Branch, Islamic Azad University
Sanandaj, Iran
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.
https://ijmc.kashanu.ac.ir/article_7608_457efe7ba6c1f3fa53a5e5327016487a.pdf
Activated carbon
Adsorption
Aliphatic alcohols
QSPR
SMF method
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2014-11-01
5
2
143
152
10.22052/ijmc.2014.7611
7611
A note on the zeroth-order general randić index of cacti and polyomino chains
Akbar Ali
akbarali.maths@gmail.com
1
Akhlaq Bhatti
akhlaq.ahmad@nu.edu.pk
2
Zahid Raza
zahid.raza@nu.edu.pk
3
National University of Computer and Emerging Sciences, Lahore-Pakistan
National University of Computer and Emerging Sciences, Lahore, Pakistan
National University of Computer and Emerging Sciences, Lahore, Pakistan
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.
https://ijmc.kashanu.ac.ir/article_7611_7ff25b2af07cf37198531204336ebb06.pdf
topological index
Zeroth-order general Randi'{c} index
Polyomino chain
Cacti