University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 Stirling Numbers and Generalized Zagreb Indices 1 5 EN T. Doslic 1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, doslic@grad.hr S. Sedghi Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran sedghi_gh@yahoo.com N. Shobe Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran nabi_shobe@yahoo.com 10.22052/ijmc.2017.15092 We 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. Simple Graph,Zagreb index,Stirling number http://ijmc.kashanu.ac.ir/article_15092.html http://ijmc.kashanu.ac.ir/article_15092_b7bb85d9dbe4ac40d6d223adc42453dd.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications 7 23 EN F. Taghvaee University of Kashan taghvaei19@yahoo.com G. Fath-Tabar University of Kashan fathtabar@kashanu.ac.ir 10.22052/ijmc.2017.15093 ABSTRACT. 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. Characteristic polynomial,Matching polynomial,Fullerene graph http://ijmc.kashanu.ac.ir/article_15093.html http://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 The Topological Indices of some Dendrimer Graphs 25 35 EN M. R. Darafsheh School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran M. Namdari Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran S. Shokrolahi Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran. shokrolahisara@yahoo.com 10.22052/ijmc.2017.15413 In 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. topological index,Dendrimer,Wiener index,Hyper Wiener index http://ijmc.kashanu.ac.ir/article_15413.html http://ijmc.kashanu.ac.ir/article_15413_df8b2c0cfc3d418f4b890e723474b4cd.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 On the Multiplicative Zagreb Indices of Bucket Recursive‎ ‎Trees 37 45 EN R. Kazemi Imam Khomeini international university r.kazemi@sci.ikiu.ac.ir 10.22052/ijmc.2017.15385 ‎Bucket 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\$‎. Bucket recursive trees‎,Multiplicative Zagreb index‎,‎Moment generating‎ ‎function‎,‎Moments http://ijmc.kashanu.ac.ir/article_15385.html http://ijmc.kashanu.ac.ir/article_15385_09d45a56a3e6e888884635bfc073bf60.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 The Conditions of the Violations of Le Chatlier’s Principle in Gas Reactions at Constant T and P 47 52 EN M. Torabi Rad University of Qom, Qom, Iran morteza.0mtr0@yahoo.com A. Abbasi University of Qom, Qom, Iran a.abbasi@qom.ac.ir 10.22052/ijmc.2016.40877 Le 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. Violation of Le Chatelier,Principle gas reaction,Mixture,Chemical equilibria,Chemical potential moderation http://ijmc.kashanu.ac.ir/article_40877.html http://ijmc.kashanu.ac.ir/article_40877_8ff2dc0bd3328b97fc4cc4983d8d533a.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 Neighbourly Irregular Derived Graphs 53 60 EN B. Basavanagoud KARNATAK UNIVERSITY DHARWAD b.basavanagoud@gmail.com S. Patil Karnatak University shreekantpatil949@gmail.com V. R. Desai Karnatak University veenardesai6f@gmail.com M. Tavakoli Ferdowsi University of Mashhad m_tavakoli@um.ac.ir A. R. Ashrafi University of Kashan ashrafi@kashanu.ac.ir 10.22052/ijmc.2016.40878 A 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. Neighbourly irregular,Derived graphs,Product graphs http://ijmc.kashanu.ac.ir/article_40878.html http://ijmc.kashanu.ac.ir/article_40878_84e728f990f1722c2fdf11f8aec1c6e0.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 Splice Graphs and their Vertex-Degree-Based Invariants 61 70 EN M. Azari Islamic Azad University mahdie.azari@gmail.com F. Falahati-Nezhad Safadasht Branch, Islamic Azad University farzanehfalahati_n@yahoo.com 10.22052/ijmc.2017.42671 Let 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. vertex degree,graph invariant,Splice http://ijmc.kashanu.ac.ir/article_42671.html http://ijmc.kashanu.ac.ir/article_42671_842a36edd0ad831bf464f22081c22654.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 An Upper Bound on the First Zagreb Index in Trees 71 82 EN R. Rasi Azarbaijan Shahid Madani University, Tabriz, Iran S. M. Sheikholeslami Azarbaijan Shahid Madani University, Tabriz, Iran A. Behmaram Institute for Research in Fundamental Sciences, Tehran, Iran behmarammath@gmail.com 10.22052/ijmc.2017.42995 In 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. First Zagreb index,First Zagreb coindex,tree,Chemical tree http://ijmc.kashanu.ac.ir/article_42995.html http://ijmc.kashanu.ac.ir/article_42995_aceaeaa2290cdaa2217a2205d4bda5af.pdf
University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 8 1 2017 03 01 Distance-Based Topological Indices and Double graph 83 91 EN M. K. Jamil ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN. m.kamran.sms@gmail.com 10.22052/ijmc.2017.43073 Let \$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. Wiener index,Harary index,Double graph http://ijmc.kashanu.ac.ir/article_43073.html http://ijmc.kashanu.ac.ir/article_43073_1e1bbd86540bb1e1baabd2a8f90bff47.pdf