University of KashanIranian Journal of Mathematical Chemistry2228-64898120170301Stirling Numbers and Generalized Zagreb Indices151509210.22052/ijmc.2017.15092ENT.Doslic1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,S.SedghiDepartment of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, IranN.ShobeDepartment of Mathematics, Babol Branch,
Islamic Azad
University, Babol, IranJournal Article20160101We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.https://ijmc.kashanu.ac.ir/article_15092_b7bb85d9dbe4ac40d6d223adc42453dd.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications7231509310.22052/ijmc.2017.15093ENF.TaghvaeeUniversity of KashanG.Fath-TabarUniversity of Kashan0000-0003-1105-3020Journal Article20160102ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matching polynomial, (-1)^km(G, k), in a regular graph. In the rest of this paper, we apply these relations for finding 5,6-matchings of fullerene graphs.https://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301The Topological Indices of some Dendrimer Graphs25351541310.22052/ijmc.2017.15413ENM. R.DarafshehSchool of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, IranM.NamdariDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranS.ShokrolahiDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20150106In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.https://ijmc.kashanu.ac.ir/article_15413_df8b2c0cfc3d418f4b890e723474b4cd.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301On the Multiplicative Zagreb Indices of Bucket Recursive Trees37451538510.22052/ijmc.2017.15385ENR.KazemiImam Khomeini international universityJournal Article20150224Bucket recursive trees are an interesting and natural generalization of ordinary recursive trees and have a connection to mathematical chemistry. In this paper, we give the lower and upper bounds for the moment generating function and moments of the multiplicative Zagreb indices in a randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$. Also, we consider the ratio of the multiplicative Zagreb indices for different values of $n$ and $b$. All our results reduce to the ordinary recursive trees for $b=1$.https://ijmc.kashanu.ac.ir/article_15385_09d45a56a3e6e888884635bfc073bf60.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301The Conditions of the Violations of Le Chatlier’s Principle in Gas Reactions at Constant T and P47524087710.22052/ijmc.2016.40877ENM.Torabi RadUniversity of Qom, Qom, IranA.AbbasiUniversity of Qom, Qom, IranJournal Article20151223Le Chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . However, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. In this article, we derived a simple equation for the violation of Le Chatelier's principle for the ideal gas reactions at the constant temperature and pressure.https://ijmc.kashanu.ac.ir/article_40877_8ff2dc0bd3328b97fc4cc4983d8d533a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301Neighbourly Irregular Derived Graphs53604087810.22052/ijmc.2016.40878ENB.BasavanagoudKARNATAK UNIVERSITY DHARWADS.PatilKarnatak UniversityV. R.DesaiKarnatak UniversityM.TavakoliFerdowsi University of MashhadA. R.AshrafiUniversity of Kashan0000-0002-2858-0663Journal Article20160309A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.https://ijmc.kashanu.ac.ir/article_40878_84e728f990f1722c2fdf11f8aec1c6e0.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301Splice Graphs and their Vertex-Degree-Based Invariants61704267110.22052/ijmc.2017.42671ENM.AzariIslamic Azad University0000-0002-0919-0598F.Falahati-NezhadSafadasht Branch, Islamic Azad UniversityJournal Article20150720Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.https://ijmc.kashanu.ac.ir/article_42671_842a36edd0ad831bf464f22081c22654.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301An Upper Bound on the First Zagreb Index in Trees71824299510.22052/ijmc.2017.42995ENR.RasiAzarbaijan Shahid Madani University, Tabriz, IranS. M.SheikholeslamiAzarbaijan Shahid Madani University, Tabriz, IranA.BehmaramInstitute for Research in Fundamental Sciences, Tehran, IranJournal Article20160301In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.https://ijmc.kashanu.ac.ir/article_42995_aceaeaa2290cdaa2217a2205d4bda5af.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898120170301Distance-Based Topological Indices and Double graph83914307310.22052/ijmc.2017.43073ENM. K.JamilABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.0000-0001-5715-9299Journal Article20150219Let $G$ be a connected graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closed-form formulas for different distance based topological indices for $D[G]$ in terms of that of $G$. Finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topological indices.https://ijmc.kashanu.ac.ir/article_43073_1e1bbd86540bb1e1baabd2a8f90bff47.pdf