Pub Date : 2020-12-01DOI: 10.22052/IJMC.2020.233343.1505
Ling Song, Li Hechao, Tang Zi-kai
The leap eccentric connectivity index of $G$ is defined as $$Lxi^{C}(G)=sum_{vin V(G)}d_{2}(v|G)e(v|G)$$ where $d_{2}(v|G) $ be the second degree of the vertex $v$ and $e(v|G)$ be the eccentricity of the vertex $v$ in $G$. In this paper, we give some properties of the leap eccentric connectivity index of the graph $G$.
{"title":"Some Properties of the Leap Eccentric Connectivity Index of Graphs","authors":"Ling Song, Li Hechao, Tang Zi-kai","doi":"10.22052/IJMC.2020.233343.1505","DOIUrl":"https://doi.org/10.22052/IJMC.2020.233343.1505","url":null,"abstract":"The leap eccentric connectivity index of $G$ is defined as $$Lxi^{C}(G)=sum_{vin V(G)}d_{2}(v|G)e(v|G)$$ where $d_{2}(v|G) $ be the second degree of the vertex $v$ and $e(v|G)$ be the eccentricity of the vertex $v$ in $G$. In this paper, we give some properties of the leap eccentric connectivity index of the graph $G$.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85111200","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 : 2020-12-01DOI: 10.22052/IJMC.2020.232036.1503
Narinder Kumar, Pawan Singh, K. Thapa, Devesh Kumar
The liquid crystal (LC) 4-4′-disubstituted biphenyls (HnCBP) of the general line formula HO-(CnH2n+1)-O-C6H4-C6H4-CN (n=1-12) shows the odd-even effect under the applied electric field. The odd-even effects are observed in the HOMO-LUMO gap, birefringence, order parameter, and dipole moment. The odd carbon atom number of alkyl chain shows HOMO-LUMO gap, birefringence and order parameter in the upward direction and even carbon atom number of alkyl chain shows in the downward direction; however the dipole moment exhibits a shift of even carbon number of alkyl chain in the upward direction and odd carbon number of alkyl chain in the downward direction.
通线式HO-(CnH2n+1)- o - c6h4 - c6h4 - cn (n=1-12)的液晶(LC) 4-4′-二取代联苯(HnCBP)在外加电场作用下表现出奇偶效应。在HOMO-LUMO隙、双折射、序参量和偶极矩等方面观察到奇偶效应。烷基链奇碳原子序数向上呈现HOMO-LUMO间隙、双折射和序参量，烷基链偶碳原子序数向下呈现;偶极矩表现为烷基链偶碳数向上移动，烷基链奇碳数向下移动。
{"title":"Odd-Even Effect Observed in the Electro-Optical Properties of the Homologous Series of HnCBP Liquid Crystal Studied under the Impact of the Electric Field: A Theoretical Approach","authors":"Narinder Kumar, Pawan Singh, K. Thapa, Devesh Kumar","doi":"10.22052/IJMC.2020.232036.1503","DOIUrl":"https://doi.org/10.22052/IJMC.2020.232036.1503","url":null,"abstract":"The liquid crystal (LC) 4-4′-disubstituted biphenyls (HnCBP) of the general line formula HO-(CnH2n+1)-O-C6H4-C6H4-CN (n=1-12) shows the odd-even effect under the applied electric field. The odd-even effects are observed in the HOMO-LUMO gap, birefringence, order parameter, and dipole moment. The odd carbon atom number of alkyl chain shows HOMO-LUMO gap, birefringence and order parameter in the upward direction and even carbon atom number of alkyl chain shows in the downward direction; however the dipole moment exhibits a shift of even carbon number of alkyl chain in the upward direction and odd carbon number of alkyl chain in the downward direction.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79982882","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 : 2020-12-01DOI: 10.22052/IJMC.2020.231652.1502
Hechao Liu, Mingyao Zeng, H. Deng, Zikai Tang
The Gutman index, Schultz index, multiplicative degree-Kirchhoff index, additive degree-Kirchhoff index are four well-studied topological indices, which are useful tools in QSPR and QSAR investigations. Spiro compounds are an important class of cycloalkanes in organic chemistry. In this paper, we determine the expected values of these indices in the random spiro chains, and the extremal values among all spiro chains with n hexagons.
{"title":"Some Indices in the Random Spiro Chains","authors":"Hechao Liu, Mingyao Zeng, H. Deng, Zikai Tang","doi":"10.22052/IJMC.2020.231652.1502","DOIUrl":"https://doi.org/10.22052/IJMC.2020.231652.1502","url":null,"abstract":"The Gutman index, Schultz index, multiplicative degree-Kirchhoff index, additive degree-Kirchhoff index are four well-studied topological indices, which are useful tools in QSPR and QSAR investigations. Spiro compounds are an important class of cycloalkanes in organic chemistry. In this paper, we determine the expected values of these indices in the random spiro chains, and the extremal values among all spiro chains with n hexagons.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75738559","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 : 2020-12-01DOI: 10.22052/IJMC.2020.240260.1514
Sadia Noureen, A. A. Bhatti, Akbar Ali
The modified first Zagreb connection index $ZC_{1}^{*}$ for a graph $G$ is defined as $ZC_{1}^{*}(G)= sum_{vin V(G)}d_{v}tau_{v},$, where $d_{v}$ is degree of the vertex $v$ and $tau _{v}$ is the connection number of $v$ (that is, the number of vertices having distance 2 from $v$). By an $n$-vertex graph, we mean a graph of order $n$. A branching vertex of a graph is a vertex with degree greater than $2$. In this paper, the graphs with maximum and minimum $ZC_{1}^{*}$ values are characterized from the class of all $n$-vertex trees with a fixed number of branching vertices.
对于图$G$，修改后的第一个萨格勒布连接索引$ZC_{1}^{*}$定义为$ZC_{1}^{*}(G)= sum_{vin V(G)}d_{V}tau_{V}，$，其中$d_{V}$是顶点$ V $的度，$ tau_{V}$是$ V $的连接数(即与$ V $的距离为2的顶点数)。我们所说的n顶点图，是指阶为n的图。图的分支顶点是度大于2的顶点。本文对具有最大和最小$ZC_{1}^{*}$值的图进行了刻画，这些图来自具有固定数目分支顶点的所有$n$顶点树的类。
{"title":"On the Modified First Zagreb Connection Index of Trees of a Fixed Order and Number of Branching Vertices","authors":"Sadia Noureen, A. A. Bhatti, Akbar Ali","doi":"10.22052/IJMC.2020.240260.1514","DOIUrl":"https://doi.org/10.22052/IJMC.2020.240260.1514","url":null,"abstract":"The modified first Zagreb connection index $ZC_{1}^{*}$ for a graph $G$ is defined as $ZC_{1}^{*}(G)= sum_{vin V(G)}d_{v}tau_{v},$, where $d_{v}$ is degree of the vertex $v$ and $tau _{v}$ is the connection number of $v$ (that is, the number of vertices having distance 2 from $v$). By an $n$-vertex graph, we mean a graph of order $n$. A branching vertex of a graph is a vertex with degree greater than $2$. In this paper, the graphs with maximum and minimum $ZC_{1}^{*}$ values are characterized from the class of all $n$-vertex trees with a fixed number of branching vertices.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86358020","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 : 2020-09-30DOI: 10.22052/IJMC.2020.225271.1497
Mingyao Zeng, Qiqi Xiao, Zikai Tang, H. Deng
For a connected graph G, the Wiener index W(G) of G is the sum of the distances of all pairs of vertices, the Kirchhoff index Kf(G) of G is the sum of the resistance distances of all pairs of vertices. A k-polygonal cactus is a connected graph in which the length of every cycle is k and any two cycles have at most one common vertex. In this paper, we give the maximum and minimum values of the Wiener index and the Kirchhoff index for all k-polygonal cacti with n cycles and determine the corresponding extremal graphs, generalize results of spiro hexagonal chains with n hexagons.
{"title":"Extremal polygonal cacti for Wiener index and Kirchhoff index","authors":"Mingyao Zeng, Qiqi Xiao, Zikai Tang, H. Deng","doi":"10.22052/IJMC.2020.225271.1497","DOIUrl":"https://doi.org/10.22052/IJMC.2020.225271.1497","url":null,"abstract":"For a connected graph G, the Wiener index W(G) of G is the sum of the distances of all pairs of vertices, the Kirchhoff index Kf(G) of G is the sum of the resistance distances of all pairs of vertices. A k-polygonal cactus is a connected graph in which the length of every cycle is k and any two cycles have at most one common vertex. In this paper, we give the maximum and minimum values of the Wiener index and the Kirchhoff index for all k-polygonal cacti with n cycles and determine the corresponding extremal graphs, generalize results of spiro hexagonal chains with n hexagons.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77248475","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 : 2020-09-01DOI: 10.22052/IJMC.2020.222023.1490
G. Shirdel, A. Mortezaee, E. Golpar-Raboky
The non-uniform hypergraph is the general hypergraph in which an edge can join any number of vertices. This makes them more applicable data structure than the uniform hypergraph and also, on the other hand, mathematical relations of the nonuniform hypergraph are usually complicated. In this paper, we study the non-uniform hypergraph more precisely and then analyze some of its spectral properties and compare them with those of the uniform hypergraph.
{"title":"Non-uniform Hypergraphs","authors":"G. Shirdel, A. Mortezaee, E. Golpar-Raboky","doi":"10.22052/IJMC.2020.222023.1490","DOIUrl":"https://doi.org/10.22052/IJMC.2020.222023.1490","url":null,"abstract":"The non-uniform hypergraph is the general hypergraph in which an edge can join any number of vertices. This makes them more applicable data structure than the uniform hypergraph and also, on the other hand, mathematical relations of the nonuniform hypergraph are usually complicated. In this paper, we study the non-uniform hypergraph more precisely and then analyze some of its spectral properties and compare them with those of the uniform hypergraph.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85375659","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 : 2020-09-01DOI: 10.22052/IJMC.2020.214829.1481
Abhay Rajpoot, Lavanya Selvaganesh
The Symmetric division deg (SDD) index is a well-established valuable index in the analysis of quantitative structure-property and structure-activity relationships for molecular graphs. In this paper, we study the range of SDD-index for special classes of trees and unicyclic graphs. We present the first four lower bounds for SDD-index of trees and unicyclic graphs, which admit a perfect matching and find the subclasses of graphs that attain these bounds. Further, we also compute the upper bounds of SDD-index for the collection of molecular graphs, namely the trees and unicyclic graphs, each having maximum degree four and that admit a perfect matching.
{"title":"Bounds of the Symmetric Division Deg Index For Trees And Unicyclic Graphs With A Perfect Matching","authors":"Abhay Rajpoot, Lavanya Selvaganesh","doi":"10.22052/IJMC.2020.214829.1481","DOIUrl":"https://doi.org/10.22052/IJMC.2020.214829.1481","url":null,"abstract":"The Symmetric division deg (SDD) index is a well-established valuable index in the analysis of quantitative structure-property and structure-activity relationships for molecular graphs. In this paper, we study the range of SDD-index for special classes of trees and unicyclic graphs. We present the first four lower bounds for SDD-index of trees and unicyclic graphs, which admit a perfect matching and find the subclasses of graphs that attain these bounds. Further, we also compute the upper bounds of SDD-index for the collection of molecular graphs, namely the trees and unicyclic graphs, each having maximum degree four and that admit a perfect matching.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76909629","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 : 2020-09-01DOI: 10.22052/IJMC.2020.160449.1413
Yu Zhao, Risong Li
In this paper we continue to study the chaotic properties of the following lattice dynamical system: bji+1= a1 g(bji)+ a2 g(bj-1i)+ a3 g(bj+1i), where i is discrete time index, j is lattice side index with system size L, g is a selfmap on [0, 1] and a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1 are coupling constants. In particular, it is shown that if g is turbulent (resp. erratic) then so is the above system, and that if there exists a g-connected family G with respect to disjointed compact subsets D1, D2, …, Dm, then there is a compact invariant set K'⊆D' such that F |K' is semi-conjugate to m-shift for any coupling constants a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1, where D' ⊆ IL is nonempty and compact. Moreover, an example and two problems are given.
{"title":"Turbulence, erratic property and horseshoes in a coupled lattice system related with Belusov-Zhabotinsky reaction","authors":"Yu Zhao, Risong Li","doi":"10.22052/IJMC.2020.160449.1413","DOIUrl":"https://doi.org/10.22052/IJMC.2020.160449.1413","url":null,"abstract":"In this paper we continue to study the chaotic properties of the following lattice dynamical system: bji+1= a1 g(bji)+ a2 g(bj-1i)+ a3 g(bj+1i), where i is discrete time index, j is lattice side index with system size L, g is a selfmap on [0, 1] and a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1 are coupling constants. In particular, it is shown that if g is turbulent (resp. erratic) then so is the above system, and that if there exists a g-connected family G with respect to disjointed compact subsets D1, D2, …, Dm, then there is a compact invariant set K'⊆D' such that F |K' is semi-conjugate to m-shift for any coupling constants a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1, where D' ⊆ IL is nonempty and compact. Moreover, an example and two problems are given.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79395827","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 : 2020-09-01DOI: 10.22052/IJMC.2020.217837.1483
Fariba Masoomi Sefiddashti, Hedayat Haddadi, S. Asadpour, Shima Ghanavati Nasab
In this study, six molecular descriptors were selected from a pool of variables using stepwise regression to built a QSAR model for a series of 2-benzyloxy benzamide derivatives as an SMS2 inhibitor to reduce atherosclerosis. Simple multiple linear regression (MLR) and a nonlinear method, artificial neural network (ANN), were used to modeling the bioactivities of the compounds. Modeling was carried out in total with 34 compounds of 2-benzyl oxybenzamide derivatives. PCA was used to divide the compounds into two groups of two training series and tests. The model was constructed with 27 combinations as training set, then the validity and predictive ability of the model were evaluated with the remaining 7 combinations. While the MLR provides an acceptable model for predictions, the ANN-based model significantly improves the predictive ability. In ANN model the average relative error (RE%) of prediction set is lower than 1% and square correlation coefficient (R2) is 0.9912.
{"title":"Prediction of IC50 Values of 2−benzyloxybenzamide Derivatives using Multiple Linear Regression and Artificial Neural Network Methods","authors":"Fariba Masoomi Sefiddashti, Hedayat Haddadi, S. Asadpour, Shima Ghanavati Nasab","doi":"10.22052/IJMC.2020.217837.1483","DOIUrl":"https://doi.org/10.22052/IJMC.2020.217837.1483","url":null,"abstract":"In this study, six molecular descriptors were selected from a pool of variables using stepwise regression to built a QSAR model for a series of 2-benzyloxy benzamide derivatives as an SMS2 inhibitor to reduce atherosclerosis. Simple multiple linear regression (MLR) and a nonlinear method, artificial neural network (ANN), were used to modeling the bioactivities of the compounds. Modeling was carried out in total with 34 compounds of 2-benzyl oxybenzamide derivatives. PCA was used to divide the compounds into two groups of two training series and tests. The model was constructed with 27 combinations as training set, then the validity and predictive ability of the model were evaluated with the remaining 7 combinations. While the MLR provides an acceptable model for predictions, the ANN-based model significantly improves the predictive ability. In ANN model the average relative error (RE%) of prediction set is lower than 1% and square correlation coefficient (R2) is 0.9912.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77962086","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 : 2020-07-01DOI: 10.22052/IJMC.2020.144902.1384
M. Medeleanu, Z. Khalaj, M. Diudea
Rhombellanes are mathematical structures existing in various environments, in crystal or quasicrystal networks, or even in their homeomorphs, further possible becoming real molecules. Rhombellanes originate in the K2.3 complete bipartite graph, a tile found in the linear polymeric staffanes. In close analogy, a rod-like polymer derived from hexahydroxy-cyclohexane, HHCH, was imagined. Further, the idea of linear polymer synthesized from dehydro-adamantane, DHAda, was extended in the design of a three-dimensional crystal network, called here Ada-Ada, of which tile is a hyper-adamantane (an adamantane of which vertices are just adamantanes). It was suggested that Ada-Ada would be synthesized starting from the real molecule tetrabromo-adamantane, by dehydrogenation and polymerization. The crystal structures herein proposed were characterized by connectivity and ring sequences and also by the Omega polynomial.
{"title":"Rhombellane-related crystal networks","authors":"M. Medeleanu, Z. Khalaj, M. Diudea","doi":"10.22052/IJMC.2020.144902.1384","DOIUrl":"https://doi.org/10.22052/IJMC.2020.144902.1384","url":null,"abstract":"Rhombellanes are mathematical structures existing in various environments, in crystal or quasicrystal networks, or even in their homeomorphs, further possible becoming real molecules. Rhombellanes originate in the K2.3 complete bipartite graph, a tile found in the linear polymeric staffanes. In close analogy, a rod-like polymer derived from hexahydroxy-cyclohexane, HHCH, was imagined. Further, the idea of linear polymer synthesized from dehydro-adamantane, DHAda, was extended in the design of a three-dimensional crystal network, called here Ada-Ada, of which tile is a hyper-adamantane (an adamantane of which vertices are just adamantanes). It was suggested that Ada-Ada would be synthesized starting from the real molecule tetrabromo-adamantane, by dehydrogenation and polymerization. The crystal structures herein proposed were characterized by connectivity and ring sequences and also by the Omega polynomial.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76702225","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：