Pub Date : 2018-03-01DOI: 10.22052/IJMC.2017.53463.1195
A. Hamzeh, A. Iranmanesh, S. Hossein-Zadeh, M. Hosseinzadeh, I. Gutman
Let G be a simple graph with vertex set V (G). The common neighborhood graph or congraph of G, denoted by con(G), is a graph with vertex set V (G), in which two vertices are adjacent if and only if they have at least one common neighbor in G. We compute the congraphs of some composite graphs. Using these results, the congraphs of several special graphs are determined.
{"title":"On common neighborhood graphs II","authors":"A. Hamzeh, A. Iranmanesh, S. Hossein-Zadeh, M. Hosseinzadeh, I. Gutman","doi":"10.22052/IJMC.2017.53463.1195","DOIUrl":"https://doi.org/10.22052/IJMC.2017.53463.1195","url":null,"abstract":"Let G be a simple graph with vertex set V (G). The common neighborhood graph or congraph of G, denoted by con(G), is a graph with vertex set V (G), in which two vertices are adjacent if and only if they have at least one common neighbor in G. We compute the congraphs of some composite graphs. Using these results, the congraphs of several special graphs are determined.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"6 1","pages":"37-46"},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75263333","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.2017.83263.1285
I. Gutman
The theoretical treatment of cycle-effects on total pi-electron energy, mainly elaborated by Nenad Trinajstic and his research group, is re-stated in a general and more formal manner. It enables to envisage several other possible ways of measuring the cycle-effects and points at further directions of research.
{"title":"General Theory of Cycle-Dependence of Total pi-Electron Energy","authors":"I. Gutman","doi":"10.22052/IJMC.2017.83263.1285","DOIUrl":"https://doi.org/10.22052/IJMC.2017.83263.1285","url":null,"abstract":"The theoretical treatment of cycle-effects on total pi-electron energy, mainly elaborated by Nenad Trinajstic and his research group, is re-stated in a general and more formal manner. It enables to envisage several other possible ways of measuring the cycle-effects and points at further directions of research.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"106 1","pages":"9-16"},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78089914","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.2017.100951.1317
J. Palacios
The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG = 2|E|/n. We also find some particular tight bounds for some classes of graphs in terms of customary graph parameters.
{"title":"More inequalities for Laplacian indices by way of majorization","authors":"J. Palacios","doi":"10.22052/IJMC.2017.100951.1317","DOIUrl":"https://doi.org/10.22052/IJMC.2017.100951.1317","url":null,"abstract":"The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG = 2|E|/n. We also find some particular tight bounds for some classes of graphs in terms of customary graph parameters.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"4 1","pages":"17-24"},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91004352","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.2017.101019.1318
M. Diudea
A regular polyhedron is a polyhedron having congruent regular polygons as faces, arranged in the same manner around identical vertices; its symmetry group acts transitively on its flags, a regular polyhedron being vertex-, edgeand face-transitive [1]. They show three symmetry groups: tetrahedral; octahedral (or cubic) and icosahedral (or dodecahedral). Any shapes with icosahedral or octahedral symmetry will also include the tetrahedral symmetry. There are five regular polyhedra, known as Platonic polyhedral solids: tetrahedron (T), cube (C), octahedron (O), dodecahedron (D) and icosahedron (I), written as {3,3}; {4,3}; {3,4}; {5,3} and {3,5} by using the basic Schlӓfli [2] symbols {p,q} where p is the number of vertices in a given face while q is the number of faces containing a given vertex.
{"title":"Hypercube related polytopes","authors":"M. Diudea","doi":"10.22052/IJMC.2017.101019.1318","DOIUrl":"https://doi.org/10.22052/IJMC.2017.101019.1318","url":null,"abstract":"A regular polyhedron is a polyhedron having congruent regular polygons as faces, arranged in the same manner around identical vertices; its symmetry group acts transitively on its flags, a regular polyhedron being vertex-, edgeand face-transitive [1]. They show three symmetry groups: tetrahedral; octahedral (or cubic) and icosahedral (or dodecahedral). Any shapes with icosahedral or octahedral symmetry will also include the tetrahedral symmetry. There are five regular polyhedra, known as Platonic polyhedral solids: tetrahedron (T), cube (C), octahedron (O), dodecahedron (D) and icosahedron (I), written as {3,3}; {4,3}; {3,4}; {5,3} and {3,5} by using the basic Schlӓfli [2] symbols {p,q} where p is the number of vertices in a given face while q is the number of faces containing a given vertex.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"30 1","pages":"1-8"},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74901435","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.2017.58647.1228
N. Dehgardi
Let $G$ be a finite and simple graph with edge set $E(G)$. The revised Szeged index is defined as $Sz^{*}(G)=sum_{e=uvin E(G)}(n_u(e|G)+frac{n_{G}(e)}{2})(n_v(e|G)+frac{n_{G}(e)}{2}),$ where $n_u(e|G)$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$ and $n_{G}(e)$ is the number of equidistant vertices of $e$ in $G$. In this paper, we compute the revised Szeged index of the join and corona product of graphs.
设$G$是一个有边集$E(G)$ $的有限简单图。修正后的塞格德指数定义为:$Sz^{*}(G)=sum_{e=uvin e (G)}(n_u(e) |G)+frac{n_{G}(e)}{2})(n_v(e|G))+frac{n_{G}(e)}{2})，其中$n_u(e|G)$表示$G$中离$u$比离$v$近的顶点数，$ n_{G}(e)$表示$G$中离$u$比离$v$近的顶点数，$ $n_{G}(e)$表示$e$在$G$中距离$e$相等的顶点数。在本文中，我们计算了图的连接和电晕积的修正塞格德指数。
{"title":"A Note on Revised Szeged Index of Graph Operations","authors":"N. Dehgardi","doi":"10.22052/IJMC.2017.58647.1228","DOIUrl":"https://doi.org/10.22052/IJMC.2017.58647.1228","url":null,"abstract":"Let $G$ be a finite and simple graph with edge set $E(G)$. The revised Szeged index is defined as $Sz^{*}(G)=sum_{e=uvin E(G)}(n_u(e|G)+frac{n_{G}(e)}{2})(n_v(e|G)+frac{n_{G}(e)}{2}),$ where $n_u(e|G)$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$ and $n_{G}(e)$ is the number of equidistant vertices of $e$ in $G$. In this paper, we compute the revised Szeged index of the join and corona product of graphs.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"563 1","pages":"57-63"},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72598104","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.2017.88790.1294
M. A. Tahan, B. Davvaz
Algebraic hyperstructures have many applications in various sciences. The main purpose of this paper is to provide a new application of weak hyperstructures in Chemistry. More precisely, we present three different examples of hyperstructures associated to electrochemical cells. In which we prove that our hyperstructures are Hv-semigroups and we present some interesting results.
{"title":"Weak Chemical Hyperstructures Associated to Electrochemical Cells","authors":"M. A. Tahan, B. Davvaz","doi":"10.22052/IJMC.2017.88790.1294","DOIUrl":"https://doi.org/10.22052/IJMC.2017.88790.1294","url":null,"abstract":"Algebraic hyperstructures have many applications in various sciences. The main purpose of this paper is to provide a new application of weak hyperstructures in Chemistry. More precisely, we present three different examples of hyperstructures associated to electrochemical cells. In which we prove that our hyperstructures are Hv-semigroups and we present some interesting results.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"25 1","pages":"65-75"},"PeriodicalIF":1.3,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72531791","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 : 2017-12-01DOI: 10.22052/IJMC.2016.39228
S. Mosazadeh
In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.
{"title":"The uniqueness theorem for inverse nodal problems with a chemical potential","authors":"S. Mosazadeh","doi":"10.22052/IJMC.2016.39228","DOIUrl":"https://doi.org/10.22052/IJMC.2016.39228","url":null,"abstract":"In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"10 1","pages":"403-411"},"PeriodicalIF":1.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85951861","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 : 2017-12-01DOI: 10.22052/IJMC.2017.29095.1109
A. HaghBin, H. Jafari
The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The obtained approximate solutions are compared with the numerical results in the literature to show the applicability, efficiency and accuracy of the method.
{"title":"Solving time-fractional chemical engineering equations by modified variational iteration method as fixed point iteration method","authors":"A. HaghBin, H. Jafari","doi":"10.22052/IJMC.2017.29095.1109","DOIUrl":"https://doi.org/10.22052/IJMC.2017.29095.1109","url":null,"abstract":"The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The obtained approximate solutions are compared with the numerical results in the literature to show the applicability, efficiency and accuracy of the method.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"55 1","pages":"365-375"},"PeriodicalIF":1.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73467418","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 : 2017-12-01DOI: 10.22052/IJMC.2017.46693.1161
M. Eliasi, A. Ghalavand
The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12.
{"title":"Extremal Trees with Respect to Some Versions of Zagreb Indices Via Majorization","authors":"M. Eliasi, A. Ghalavand","doi":"10.22052/IJMC.2017.46693.1161","DOIUrl":"https://doi.org/10.22052/IJMC.2017.46693.1161","url":null,"abstract":"The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"483 1","pages":"391-401"},"PeriodicalIF":1.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77795632","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 : 2017-12-01DOI: 10.22052/IJMC.2017.53731.1198
R. Kazemi
The first multiplicative Zagreb index $Pi_1(G)$ is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index $Pi_2(G)$ is equal to the product of the products of the degree of pairs of adjacent vertices of the underlying molecular graphs $G$. Also, the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of the sums of the degree of pairs of adjacent vertices of $G$. In this paper, we introduce a new version of the multiplicative sum Zagreb index and study the moments of the ratio and product of all above indices in a randomly chosen molecular graph with tree structure of order $n$. Also, a supermartingale is introduced by Doob's supermartingale inequality.
{"title":"The ratio and product of the multiplicative Zagreb indices","authors":"R. Kazemi","doi":"10.22052/IJMC.2017.53731.1198","DOIUrl":"https://doi.org/10.22052/IJMC.2017.53731.1198","url":null,"abstract":"The first multiplicative Zagreb index $Pi_1(G)$ is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index $Pi_2(G)$ is equal to the product of the products of the degree of pairs of adjacent vertices of the underlying molecular graphs $G$. Also, the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of the sums of the degree of pairs of adjacent vertices of $G$. In this paper, we introduce a new version of the multiplicative sum Zagreb index and study the moments of the ratio and product of all above indices in a randomly chosen molecular graph with tree structure of order $n$. Also, a supermartingale is introduced by Doob's supermartingale inequality.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":"2 1","pages":"377-390"},"PeriodicalIF":1.3,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74522453","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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