Pub Date : 2017-06-22DOI: 10.22052/IJMC.2017.83138.1284
B. Basavanagoud, Shreekant Patil, H. Deng
Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zagreb index, is better than models corresponding to the first Zagreb index and F-index. Further, we compute the second order first Zagreb index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q], tadpole graphs, wheel graphs and ladder graphs.
{"title":"On the second order first zagreb index","authors":"B. Basavanagoud, Shreekant Patil, H. Deng","doi":"10.22052/IJMC.2017.83138.1284","DOIUrl":"https://doi.org/10.22052/IJMC.2017.83138.1284","url":null,"abstract":"Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zagreb index, is better than models corresponding to the first Zagreb index and F-index. Further, we compute the second order first Zagreb index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q], tadpole graphs, wheel graphs and ladder graphs.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81505189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/ijmc.2017.43095
R. Todeschini
{"title":"Autobiography of Roberto Todeschini","authors":"R. Todeschini","doi":"10.22052/ijmc.2017.43095","DOIUrl":"https://doi.org/10.22052/ijmc.2017.43095","url":null,"abstract":"","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78467198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/IJMC.2017.27307.1101
A. Mohajeri, P. Manshour, M. Mousaee
In this paper, a novel topological index, named M-index, is introduced based on expanded form of the Wiener matrix. For constructing this index the atomic characteristics and the interaction of the vertices in a molecule are taken into account. The usefulness of the M-index is demonstrated by several QSPR/QSAR models for different physico-chemical properties and biological activities of a large number of diversified compounds. Moreover, the applicability of the proposed index has been checked among isomeric compounds. In each case the stability of the obtained model is confirmed by the cross validation test. The results of present study indicate that the M-index provides a promising route for developing highly correlated QSPR/QSAR models. On the other hand, the M-index is easy to generate and the developed QSPR/QSAR models based on this index are linearly correlated. This is an interesting feature of the M-index when compared with quantum chemical descriptors which require vast computational cost and exhibit limitations for large sized molecules.
{"title":"A novel topological descriptor based on the expanded wiener index: Applications to QSPR/QSAR studies","authors":"A. Mohajeri, P. Manshour, M. Mousaee","doi":"10.22052/IJMC.2017.27307.1101","DOIUrl":"https://doi.org/10.22052/IJMC.2017.27307.1101","url":null,"abstract":"In this paper, a novel topological index, named M-index, is introduced based on expanded form of the Wiener matrix. For constructing this index the atomic characteristics and the interaction of the vertices in a molecule are taken into account. The usefulness of the M-index is demonstrated by several QSPR/QSAR models for different physico-chemical properties and biological activities of a large number of diversified compounds. Moreover, the applicability of the proposed index has been checked among isomeric compounds. In each case the stability of the obtained model is confirmed by the cross validation test. The results of present study indicate that the M-index provides a promising route for developing highly correlated QSPR/QSAR models. On the other hand, the M-index is easy to generate and the developed QSPR/QSAR models based on this index are linearly correlated. This is an interesting feature of the M-index when compared with quantum chemical descriptors which require vast computational cost and exhibit limitations for large sized molecules.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75577048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/IJMC.2017.80007.1275
M. Darafsheh, R. Modabernia, M. Namdari
ABSTRACT Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The Szeged index of G is defined by where respectively is the number of vertices of G closer to u (respectively v) than v (respectively u). If S is a set of size let V be the set of all subsets of S of size 3. Then we define three types of intersection graphs with vertex set V. These graphs are denoted by and we will find their Szeged indices.
{"title":"Computing Szeged Index of Graphs on Triples","authors":"M. Darafsheh, R. Modabernia, M. Namdari","doi":"10.22052/IJMC.2017.80007.1275","DOIUrl":"https://doi.org/10.22052/IJMC.2017.80007.1275","url":null,"abstract":"ABSTRACT Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The Szeged index of G is defined by where respectively is the number of vertices of G closer to u (respectively v) than v (respectively u). If S is a set of size let V be the set of all subsets of S of size 3. Then we define three types of intersection graphs with vertex set V. These graphs are denoted by and we will find their Szeged indices.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81463517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/IJMC.2017.58461.1225
E. Mohammadinasab
This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. Multiple linear regression was used to estimate the correlation between these critical properties and molecular descriptors using proper coefficients. To achieve this aim, the most appropriate molecular descriptors were chosen from among 11 structural and geometric descriptors in order to determine the critical properties of the intended molecules. The results showed that among all the proposed models to predict critical temperature, pressure and volume, a model including the combination of such descriptors as HyperWiener, Platt, MinZL is the most appropriate one.
{"title":"Determination of critical properties of Alkanes derivatives using multiple linear regression","authors":"E. Mohammadinasab","doi":"10.22052/IJMC.2017.58461.1225","DOIUrl":"https://doi.org/10.22052/IJMC.2017.58461.1225","url":null,"abstract":"This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. Multiple linear regression was used to estimate the correlation between these critical properties and molecular descriptors using proper coefficients. To achieve this aim, the most appropriate molecular descriptors were chosen from among 11 structural and geometric descriptors in order to determine the critical properties of the intended molecules. The results showed that among all the proposed models to predict critical temperature, pressure and volume, a model including the combination of such descriptors as HyperWiener, Platt, MinZL is the most appropriate one.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83428913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/IJMC.2017.67735.1254
Z. Wang, Y. Mao, X. Wang, C. Wang
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the emph{Steiner distance} $d_G(S)$ of the vertices of $S$ is the minimum size of a connected subgraph whose vertex set contains $S$. Recently, Furtula, Gutman, and Katani'{c} introduced the concept of Steiner Harary index and gave its chemical applications. The emph{$k$-center Steiner Harary index} $SH_k(G)$ of $G$ is defined by $SH_k(G)=sum_{Ssubseteq V(G),|S|=k}frac{1}{d_G(S)}$. In this paper, we get the sharp upper and lower bounds for $SH_k(G)+SH_k(overline{G})$ and $SH_k(G)cdot SH_k(overline{G})$, valid for any connected graph $G$ whose complement $overline {G}$ is also connected.
{"title":"Nordhaus-Gaddum type results for the Harary index of graphs","authors":"Z. Wang, Y. Mao, X. Wang, C. Wang","doi":"10.22052/IJMC.2017.67735.1254","DOIUrl":"https://doi.org/10.22052/IJMC.2017.67735.1254","url":null,"abstract":"The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the emph{Steiner distance} $d_G(S)$ of the vertices of $S$ is the minimum size of a connected subgraph whose vertex set contains $S$. Recently, Furtula, Gutman, and Katani'{c} introduced the concept of Steiner Harary index and gave its chemical applications. The emph{$k$-center Steiner Harary index} $SH_k(G)$ of $G$ is defined by $SH_k(G)=sum_{Ssubseteq V(G),|S|=k}frac{1}{d_G(S)}$. In this paper, we get the sharp upper and lower bounds for $SH_k(G)+SH_k(overline{G})$ and $SH_k(G)cdot SH_k(overline{G})$, valid for any connected graph $G$ whose complement $overline {G}$ is also connected.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75778894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/IJMC.2017.44718
H. R. Tabrizidooz, M. Pourbabaee, M. Hedayati
In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching times appear as unknown parameters. Using the Legendre-Gauss-Lobatto quadrature and the corresponding differentiation matrix, the alternative problem is discretized to a nonlinear programming problem. At last, we examine three examples in order to illustrate the efficiency of the proposed method.
{"title":"Optimal control of switched systems by a modified pseudo spectral method","authors":"H. R. Tabrizidooz, M. Pourbabaee, M. Hedayati","doi":"10.22052/IJMC.2017.44718","DOIUrl":"https://doi.org/10.22052/IJMC.2017.44718","url":null,"abstract":"In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching times appear as unknown parameters. Using the Legendre-Gauss-Lobatto quadrature and the corresponding differentiation matrix, the alternative problem is discretized to a nonlinear programming problem. At last, we examine three examples in order to illustrate the efficiency of the proposed method.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80145623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/IJMC.2017.49481.1177
Inci Gültekin, B. Şahin
In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag nonbranched catacondensed benzenid chains and their corresponding caterpillar trees.
本文研究了苯类化合物链的凯库勒结构。已经证明了B_n (x) morgan - voce多项式的系数等于具有N=2n+1个点的路径图的k匹配数(m(G,k))。得到了规则之字形非支链苯链与morgan - voice多项式的关系，以及规则之字形非支链苯链与其对应的履带树的关系。
{"title":"Some relations between Kekule structure and Morgan-Voyce polynomials","authors":"Inci Gültekin, B. Şahin","doi":"10.22052/IJMC.2017.49481.1177","DOIUrl":"https://doi.org/10.22052/IJMC.2017.49481.1177","url":null,"abstract":"In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag nonbranched catacondensed benzenid chains and their corresponding caterpillar trees.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75747619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-01DOI: 10.22052/IJMC.2017.62671.1243
A. Shokri, M. Tahmourasi
A new two-step implicit linear Obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multistep methods. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.
{"title":"A new two-step Obrechkoff method with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrodinger equation and related IVPs with oscillating solutions","authors":"A. Shokri, M. Tahmourasi","doi":"10.22052/IJMC.2017.62671.1243","DOIUrl":"https://doi.org/10.22052/IJMC.2017.62671.1243","url":null,"abstract":"A new two-step implicit linear Obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multistep methods. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81012388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-03-01DOI: 10.22052/IJMC.2017.15093
F. Taghvaee, G. Fath-Tabar
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.
{"title":"Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications","authors":"F. Taghvaee, G. Fath-Tabar","doi":"10.22052/IJMC.2017.15093","DOIUrl":"https://doi.org/10.22052/IJMC.2017.15093","url":null,"abstract":"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.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80793433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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