University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101The eccentric connectivity index of bucket recursive trees7783567110.22052/ijmc.2014.5671ENRamin KazemiImam Khomeini international universityJournal Article20130806If $G$ 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.University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101Altan derivatives of a graph8590612710.22052/ijmc.2014.6127ENIvan GutmanFaculty of Science, University of Kragujevac, Kragujevac, SerbiaJournal Article20140824Altan 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.University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101Upper and lower bounds of symmetric division deg index9198735710.22052/ijmc.2014.7357ENAlexander VasilyevUniversity of Primorska, IAMJournal Article20140702Symmetric 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.University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101Polygonal tiling of some surfaces containing fullerene molecules99105737510.22052/ijmc.2014.7375ENAli Asghar RezaeiUniversity of KashanJournal Article20140924A 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.University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101On the reliability wiener number107118737710.22052/ijmc.2014.7377ENDarja Rupnik PoklukarUniversity of LjubljanaJanez ZerovnikUniversity of LjubljanaJournal Article20140417One 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.University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101Estimation of pigment magnitudes in synthetic leather by using scanner and artificial neural network119125759210.22052/ijmc.2014.7592ENPeyman ValipourIslamic Azad University of Ghaemshahr branchMansour MafiIslamic Azad University of Kashan branchMahshid FaridiIslamic Azad University of Kashan branchJournal Article20140707In 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.University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101Prediction of the adsorption capability onto activated carbon of liquid aliphatic alcohols using molecular fragments method127142760810.22052/ijmc.2014.7608ENSaadi SaaidpourSaadi Saaidpour, PhD
Assistant Professor of Analytical Chemistry
Chemistry Department,Faculty of Science
Sanandaj Branch, Islamic Azad University
Sanandaj, IranJournal Article20141002Quantitative 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.University of KashanIranian Journal of Mathematical Chemistry2228-64895220141101A note on the zeroth-order general randić index of cacti and polyomino chains143152761110.22052/ijmc.2014.7611ENAkbar AliNational University of Computer and Emerging Sciences, Lahore-Pakistan0000-0001-8160-4196Akhlaq AhmadBhattiNational University of Computer and
Emerging Sciences, Lahore, PakistanZahid RazaNational University of Computer and
Emerging Sciences, Lahore, PakistanJournal Article20141013The 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.