Pub Date : 2020-03-01DOI: 10.22052/IJMC.2020.212363.1477
Vale Arabzadeh, M. Sohrabi, N. Goudarzi, M. Davallo
In the present paper, the simultaneous spectrophotometric estimation of Metformin (MET) and Pioglitazone (PIO) in an antidiabetic drug called Actoplus MET based on least squares support vector machine (LS-SVM) was proposed. The optimum gamma (γ) and sigma (σ) parameters were found to be 825 and 90 with the root mean square error (RMSE) of 0.1343for MET, as well as 1000 and 350 with RMSE=0.4120 for PIO. Also, the mean recovery values of MET and PIO were 99.81% and 100.19%, respectively. Ultimately, the real sample was analyzed by High-Performance Liquid Chromatography (HPLC) reference method and the proposed procedure. Then, one-way analysis of variance (ANOVA) test at the 95 % confidence level was performed on achieved results from HPLC and LS-SVM methods. The statistical data of these methods showed that there were no significant differences between them.
{"title":"A Robust Spectrophotometric Method using Least Squares Support Vector Machine for Simultaneous Determination of Anti−Diabetic Drugs and Comparison with the Chromatographic Method","authors":"Vale Arabzadeh, M. Sohrabi, N. Goudarzi, M. Davallo","doi":"10.22052/IJMC.2020.212363.1477","DOIUrl":"https://doi.org/10.22052/IJMC.2020.212363.1477","url":null,"abstract":"In the present paper, the simultaneous spectrophotometric estimation of Metformin (MET) and Pioglitazone (PIO) in an antidiabetic drug called Actoplus MET based on least squares support vector machine (LS-SVM) was proposed. The optimum gamma (γ) and sigma (σ) parameters were found to be 825 and 90 with the root mean square error (RMSE) of 0.1343for MET, as well as 1000 and 350 with RMSE=0.4120 for PIO. Also, the mean recovery values of MET and PIO were 99.81% and 100.19%, respectively. Ultimately, the real sample was analyzed by High-Performance Liquid Chromatography (HPLC) reference method and the proposed procedure. Then, one-way analysis of variance (ANOVA) test at the 95 % confidence level was performed on achieved results from HPLC and LS-SVM methods. The statistical data of these methods showed that there were no significant differences between them.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88393849","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 : 2019-12-01DOI: 10.22052/IJMC.2019.174722.1432
M. Azari, Farzaneh Falahati-Nezhed
The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalities for the forgotten topological coindex in terms of some graph parameters such as the order, size, number of pendent vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree. We also study the relation between this invariant and some well-known graph invariants such as the Zagreb indices and coindices, multiplicative Zagreb indices and coindices, Zagreb eccentricity indices, eccentric connectivity index and coindex, and total eccentricity. Exact formulae for computing the forgotten topological coindex of double graphs and extended double cover of a given graph are also proposed.
{"title":"Some Results on Forgotten Topological Coindex","authors":"M. Azari, Farzaneh Falahati-Nezhed","doi":"10.22052/IJMC.2019.174722.1432","DOIUrl":"https://doi.org/10.22052/IJMC.2019.174722.1432","url":null,"abstract":"The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalities for the forgotten topological coindex in terms of some graph parameters such as the order, size, number of pendent vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree. We also study the relation between this invariant and some well-known graph invariants such as the Zagreb indices and coindices, multiplicative Zagreb indices and coindices, Zagreb eccentricity indices, eccentric connectivity index and coindex, and total eccentricity. Exact formulae for computing the forgotten topological coindex of double graphs and extended double cover of a given graph are also proposed.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77148689","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 : 2019-12-01DOI: 10.22052/IJMC.2019.191800.1447
Taylor Short, Zachary Ash
A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also determine recurrences and generating functions for the sequences enumerating maximal matchings in several specific types of polyphenylenes and use these results to analyze the asymptotic behavior.
{"title":"The number of maximal matchings in polyphenylene chains","authors":"Taylor Short, Zachary Ash","doi":"10.22052/IJMC.2019.191800.1447","DOIUrl":"https://doi.org/10.22052/IJMC.2019.191800.1447","url":null,"abstract":"A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also determine recurrences and generating functions for the sequences enumerating maximal matchings in several specific types of polyphenylenes and use these results to analyze the asymptotic behavior.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73372849","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 : 2019-12-01DOI: 10.22052/IJMC.2019.169508.1420
M. Ghorbani, Shaghayegh Rahmani, O. Ori
For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABCGG =sum_{e=uv} sqrt{f(u,v)}, where f(u,v)= (nu+nv-2)/nunvThe aim of this paper is to give some new results on this graph invariant. We also calculate the ABCGG of an infinite family of fullerenes.
{"title":"On the Graovac-Ghorbani index","authors":"M. Ghorbani, Shaghayegh Rahmani, O. Ori","doi":"10.22052/IJMC.2019.169508.1420","DOIUrl":"https://doi.org/10.22052/IJMC.2019.169508.1420","url":null,"abstract":"For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABCGG =sum_{e=uv} sqrt{f(u,v)}, where f(u,v)= (nu+nv-2)/nunvThe aim of this paper is to give some new results on this graph invariant. We also calculate the ABCGG of an infinite family of fullerenes.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80623242","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 : 2019-12-01DOI: 10.22052/IJMC.2019.191865.1448
Ozge Colakoglu Havare
Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative Structure-Property Relationship) models were designed using the Gutman index, the product connectivity Banhatti index, the Variance of degree index, and the Sigma index to predict the thermodynamic properties of monocarboxylic acids. The relationship analyses between the thermodynamic properties and the topological indices were done by using the curvilinear regression method. It is used with the linear, quadratic and cubic equations of the curvilinear regression model. These regression models were then compared.
{"title":"QSPR Analysis with Curvilinear Regression Modeling and Topological Indices","authors":"Ozge Colakoglu Havare","doi":"10.22052/IJMC.2019.191865.1448","DOIUrl":"https://doi.org/10.22052/IJMC.2019.191865.1448","url":null,"abstract":"Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative Structure-Property Relationship) models were designed using the Gutman index, the product connectivity Banhatti index, the Variance of degree index, and the Sigma index to predict the thermodynamic properties of monocarboxylic acids. The relationship analyses between the thermodynamic properties and the topological indices were done by using the curvilinear regression method. It is used with the linear, quadratic and cubic equations of the curvilinear regression model. These regression models were then compared.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88538648","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 : 2019-12-01DOI: 10.22052/IJMC.2019.200349.1460
Hechao Liu, L. You, Zikai Tang
The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of edges of G lying closer to vertex v than to vertex u, and the number of edges equidistant to u and v. In this paper, we give an effective method for computing the revised edge-Szeged index of unicyclic graphs and using this result we identify the minimum revised edge-Szeged index of conjugated unicyclic graphs (i.e., unicyclic graphs with a perfect matching). We also give a method of calculating revised edge-Szeged index of the joint graph.
连通图$G$的修正edge- seeged指数定义为Sze*(G)=∑e=uv e (G)((mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2))，其中mu(e|G)、mv(e|G)、m0(e|G)分别是G离顶点u比离顶点v近的边数、G离顶点v比离顶点u近的边数、G离顶点v比离顶点u近的边数、G离顶点u和v等距的边数。给出了计算单环图修正边-塞格德指数的一种有效方法，并利用这一结果确定了共轭单环图(即具有完美匹配的单环图)的最小修正边-塞格德指数。给出了一种计算联合图修正边-塞格德指数的方法。
{"title":"On the Revised Edge-Szeged Index of Graphs","authors":"Hechao Liu, L. You, Zikai Tang","doi":"10.22052/IJMC.2019.200349.1460","DOIUrl":"https://doi.org/10.22052/IJMC.2019.200349.1460","url":null,"abstract":"The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of edges of G lying closer to vertex v than to vertex u, and the number of edges equidistant to u and v. In this paper, we give an effective method for computing the revised edge-Szeged index of unicyclic graphs and using this result we identify the minimum revised edge-Szeged index of conjugated unicyclic graphs (i.e., unicyclic graphs with a perfect matching). We also give a method of calculating revised edge-Szeged index of the joint graph.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74117566","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 : 2019-12-01DOI: 10.22052/IJMC.2019.195759.1456
Fazal Hayat
The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for ABCa index for cacti of order $n$ with fixed number of cycles and for cacti of order $n$ with given number of pendant vertices. Furthermore, we identify all the cacti that achieve the bounds.
{"title":"On Generalized Atom-bond Connectivity Index of Cacti","authors":"Fazal Hayat","doi":"10.22052/IJMC.2019.195759.1456","DOIUrl":"https://doi.org/10.22052/IJMC.2019.195759.1456","url":null,"abstract":"The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for ABCa index for cacti of order $n$ with fixed number of cycles and for cacti of order $n$ with given number of pendant vertices. Furthermore, we identify all the cacti that achieve the bounds.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76898671","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 : 2019-09-01DOI: 10.22052/IJMC.2017.84168.1287
C. Adhikari, B. K. Mishra
The Bertz indices, derived by counting the number of connecting edges of line graphs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular descriptor has been derived from the weighted line graph of the molecular structure and applied in correlating the physicochemical properties of alkane isomers with these descriptors. A weight is tagged at the vertex of the line graph, which consequently modifies the weight of the edge. These descriptors were found to classify the alkane isomers and served well in deriving the QSPR models for various physicochemical properties. The mathematical calculations include the quantitative treatment on the role of substituents (alkyl) in governing the properties under study of the alkane isomers. Further, the use of weighted line graph in the enumeration of the topological index opens up a new vista on application to heteroatomic systems.
{"title":"A Novel Molecular Descriptor Derived from Weighted Line Graph","authors":"C. Adhikari, B. K. Mishra","doi":"10.22052/IJMC.2017.84168.1287","DOIUrl":"https://doi.org/10.22052/IJMC.2017.84168.1287","url":null,"abstract":"The Bertz indices, derived by counting the number of connecting edges of line graphs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular descriptor has been derived from the weighted line graph of the molecular structure and applied in correlating the physicochemical properties of alkane isomers with these descriptors. A weight is tagged at the vertex of the line graph, which consequently modifies the weight of the edge. These descriptors were found to classify the alkane isomers and served well in deriving the QSPR models for various physicochemical properties. The mathematical calculations include the quantitative treatment on the role of substituents (alkyl) in governing the properties under study of the alkane isomers. Further, the use of weighted line graph in the enumeration of the topological index opens up a new vista on application to heteroatomic systems.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86201042","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 : 2019-09-01DOI: 10.22052/IJMC.2017.34313.1132
C. Adiga, M. Raju, Rakshith Billava Ramanna, Anitha Narasimhamurthy
In this paper, we compute the Wiener index, first Zagreb index, second Zagreb index, degree distance index and Gutman index of edge corona of two graphs. Also in some cases we derive formulas for Weiner index, Zagreb indices, degree distance and Gutman index in terms of vertices and edges .
{"title":"Some Topological Indices of Edge Corona of Two Graphs","authors":"C. Adiga, M. Raju, Rakshith Billava Ramanna, Anitha Narasimhamurthy","doi":"10.22052/IJMC.2017.34313.1132","DOIUrl":"https://doi.org/10.22052/IJMC.2017.34313.1132","url":null,"abstract":"In this paper, we compute the Wiener index, first Zagreb index, second Zagreb index, degree distance index and Gutman index of edge corona of two graphs. Also in some cases we derive formulas for Weiner index, Zagreb indices, degree distance and Gutman index in terms of vertices and edges .","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84989273","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 : 2019-09-01DOI: 10.22052/IJMC.2019.149094.1392
M. Iranmanesh, Razieh Nejati
Abstract. Let G = (V,E) be a fi nite and simple graph with λ1, λ2,...,λn as its eigenvalues.The Estrada index of G is EE(G) =∑ni=1e^{λi} . A spiro compound is a chemical compound that presents a twisted structure of two or more rings, in which 2 or 3 rings are linked together by one common atom. In this paper, we show that the symmetric and stable spiro compounds among all spiro compounds have the minimum Estrada index.
{"title":"The Minimum Estrada Index of Spiro Compounds with k Quadrangles","authors":"M. Iranmanesh, Razieh Nejati","doi":"10.22052/IJMC.2019.149094.1392","DOIUrl":"https://doi.org/10.22052/IJMC.2019.149094.1392","url":null,"abstract":"Abstract. Let G = (V,E) be a fi nite and simple graph with λ1, λ2,...,λn as its eigenvalues.The Estrada index of G is EE(G) =∑ni=1e^{λi} . A spiro compound is a chemical compound that presents a twisted structure of two or more rings, in which 2 or 3 rings are linked together by one common atom. In this paper, we show that the symmetric and stable spiro compounds among all spiro compounds have the minimum Estrada index.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77227278","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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