Pub Date : 2018-09-01DOI: 10.22052/IJMC.2018.118091.1342
D. Vukićević, Z. Yarahmadi
Recently, one-two descriptor has been defined and it has been shown that it is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). In this paper, we analyze its generalizations by replacing the value 2 by arbitrary positive value . We show that these analyses may be on interest, because even good predictions of CP and TSA can be slightly improved. Furthermore, it can be expected that this more general descriptor can find a wider range of application than the original one. The extremal values of trees have been found for all values of .
{"title":"One-Alpha Descriptor","authors":"D. Vukićević, Z. Yarahmadi","doi":"10.22052/IJMC.2018.118091.1342","DOIUrl":"https://doi.org/10.22052/IJMC.2018.118091.1342","url":null,"abstract":"Recently, one-two descriptor has been defined and it has been shown that it is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). In this paper, we analyze its generalizations by replacing the value 2 by arbitrary positive value . We show that these analyses may be on interest, because even good predictions of CP and TSA can be slightly improved. Furthermore, it can be expected that this more general descriptor can find a wider range of application than the original one. The extremal values of trees have been found for all values of .","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82829369","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 : 2018-06-01DOI: 10.22052/IJMC.2017.96064.1309
J. Palacios
Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.
{"title":"Some Remarks on the Arithmetic-geometric Index","authors":"J. Palacios","doi":"10.22052/IJMC.2017.96064.1309","DOIUrl":"https://doi.org/10.22052/IJMC.2017.96064.1309","url":null,"abstract":"Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89459580","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 : 2018-06-01DOI: 10.22052/IJMC.2017.93637.1303
S. Zangi, M. Ghorbani, M. Eslampour
The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.
{"title":"On the eigenvalues of some matrices based on vertex degree","authors":"S. Zangi, M. Ghorbani, M. Eslampour","doi":"10.22052/IJMC.2017.93637.1303","DOIUrl":"https://doi.org/10.22052/IJMC.2017.93637.1303","url":null,"abstract":"The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82170830","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 : 2018-06-01DOI: 10.22052/IJMC.2018.108515.1327
M. Tavakoli
Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.
{"title":"Further Results on Betweenness Centrality of Graphs","authors":"M. Tavakoli","doi":"10.22052/IJMC.2018.108515.1327","DOIUrl":"https://doi.org/10.22052/IJMC.2018.108515.1327","url":null,"abstract":"Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72430712","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 : 2018-06-01DOI: 10.22052/IJMC.2018.44232.1153
R. Nasiri, H. R. Ellahi, A. Gholami, G. Fath-Tabar
For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.
{"title":"The irregularity and total irregularity of Eulerian graphs","authors":"R. Nasiri, H. R. Ellahi, A. Gholami, G. Fath-Tabar","doi":"10.22052/IJMC.2018.44232.1153","DOIUrl":"https://doi.org/10.22052/IJMC.2018.44232.1153","url":null,"abstract":"For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76545031","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 : 2018-06-01DOI: 10.22052/IJMC.2017.53844.1200
F. Safa
In this work, novel atom-type-based topological indices, named AT indices, were presented as descriptors to encode structural information of a molecule at the atomic level. The descriptors were successfully used for simultaneous quantitative structure-retention relationship (QSRR) modeling of saturated alcohols on different stationary phases (SE-30, OV-3, OV-7, OV-11, OV-17 and OV-25). At first, multiple linear regression models for Kovats retention index (RI) of alcohols on each stationary phase were separately developed using AT and Randic’s first-order molecular connectivity (1χ) indices. Adjusted correlation coefficient (R2adj) and standard error (SE) for the models were in the range of 0.994-0.999 and 4.40-8.90, respectively. Statistical validity of the models were verified by leave-one-out cross validation (R2cv > 0.99). In the next step, whole RI values on the stationary phases were combined to generate a new data set. Then, a unified model, added McReynolds polarity term as a descriptor, was developed for the new data set and the results were satisfactory (R2adj=0.995 and SE=8.55). External validation of the model resulted in the average values of 8.29 and 8.69 for standard errors of calibration and prediction, respectively. The topological indices well covered the molecular properties known to be relevant for retention indices of the model compounds.
{"title":"Novel Atom-Type-Based Topological Descriptors for Simultaneous Prediction of Gas Chromatographic Retention Indices of Saturated Alcohols on Different Stationary Phases","authors":"F. Safa","doi":"10.22052/IJMC.2017.53844.1200","DOIUrl":"https://doi.org/10.22052/IJMC.2017.53844.1200","url":null,"abstract":"In this work, novel atom-type-based topological indices, named AT indices, were presented as descriptors to encode structural information of a molecule at the atomic level. The descriptors were successfully used for simultaneous quantitative structure-retention relationship (QSRR) modeling of saturated alcohols on different stationary phases (SE-30, OV-3, OV-7, OV-11, OV-17 and OV-25). At first, multiple linear regression models for Kovats retention index (RI) of alcohols on each stationary phase were separately developed using AT and Randic’s first-order molecular connectivity (1χ) indices. Adjusted correlation coefficient (R2adj) and standard error (SE) for the models were in the range of 0.994-0.999 and 4.40-8.90, respectively. Statistical validity of the models were verified by leave-one-out cross validation (R2cv > 0.99). In the next step, whole RI values on the stationary phases were combined to generate a new data set. Then, a unified model, added McReynolds polarity term as a descriptor, was developed for the new data set and the results were satisfactory (R2adj=0.995 and SE=8.55). External validation of the model resulted in the average values of 8.29 and 8.69 for standard errors of calibration and prediction, respectively. The topological indices well covered the molecular properties known to be relevant for retention indices of the model compounds.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87908298","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 : 2018-06-01DOI: 10.22052/IJMC.2018.98655.1313
M. Faghani, E. Pourhadi
The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the number of triangles in graph.
{"title":"A note on the bounds of Laplacian-energy-like-invariant","authors":"M. Faghani, E. Pourhadi","doi":"10.22052/IJMC.2018.98655.1313","DOIUrl":"https://doi.org/10.22052/IJMC.2018.98655.1313","url":null,"abstract":"The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the number of triangles in graph.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89591253","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 : 2018-06-01DOI: 10.22052/ijmc.2017.56982.1233
A. Huber
In this paper an alternative model allowing the extension of the Debye-Huckel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads to a reformulation of the meaning of the nonlinear Poisson-Boltzmann Equation (PBE). If a concentration and/or flux gradient of particles is considered the original structure of the PBE will be modified leading to a nonlinear partial differential equation (nPDE) of the third order. It is shown how one can derive classes of solutions for the potential function analytically by application of pure algebraic steps. The benefit of the mathematical tools used here is the fact that closed-form solutions can be calculated and thus, numerical methods are not necessary. The important outcome of the present study is twofold meaningful: (i) The model equation allows the description of time dependent problems in the theory of ions, and (ii) the mathematical procedure can be used to derive classes of solutions of arbitrary nPDEs, especially those of higher order.
{"title":"An algebraic calculation method for describing time-dependent processes in electrochemistry – Expansion of existing procedures","authors":"A. Huber","doi":"10.22052/ijmc.2017.56982.1233","DOIUrl":"https://doi.org/10.22052/ijmc.2017.56982.1233","url":null,"abstract":"In this paper an alternative model allowing the extension of the Debye-Huckel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads to a reformulation of the meaning of the nonlinear Poisson-Boltzmann Equation (PBE). If a concentration and/or flux gradient of particles is considered the original structure of the PBE will be modified leading to a nonlinear partial differential equation (nPDE) of the third order. It is shown how one can derive classes of solutions for the potential function analytically by application of pure algebraic steps. The benefit of the mathematical tools used here is the fact that closed-form solutions can be calculated and thus, numerical methods are not necessary. The important outcome of the present study is twofold meaningful: (i) The model equation allows the description of time dependent problems in the theory of ions, and (ii) the mathematical procedure can be used to derive classes of solutions of arbitrary nPDEs, especially those of higher order.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85127015","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 : 2018-03-01DOI: 10.22052/IJMC.2017.59425.1231
Yasar Nacaroglu, A. D. Maden
In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.
{"title":"On the Eccentric Connectivity Index of Unicyclic Graphs","authors":"Yasar Nacaroglu, A. D. Maden","doi":"10.22052/IJMC.2017.59425.1231","DOIUrl":"https://doi.org/10.22052/IJMC.2017.59425.1231","url":null,"abstract":"In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89562764","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 : 2018-03-01DOI: 10.22052/IJMC.2017.48936.1175
H. Bashiri, A. Sahjari
The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is shown that the kinetic of adsorption onto multi-walled carbon nanotube can be used to obtain its spectral dimension, successfully.
{"title":"Fractal-Like Kinetics Study of Adsorption on Multi-walled Carbon Nanotube","authors":"H. Bashiri, A. Sahjari","doi":"10.22052/IJMC.2017.48936.1175","DOIUrl":"https://doi.org/10.22052/IJMC.2017.48936.1175","url":null,"abstract":"The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is shown that the kinetic of adsorption onto multi-walled carbon nanotube can be used to obtain its spectral dimension, successfully.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74381797","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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