Pub Date : 2020-07-01DOI: 10.22052/IJMC.2020.224324.1493
A. Shokri, M. M. Khalsaraei, Ali Atashyar
In this paper, a new two-step hybrid method of twelfth algebraic order is constructed and analyzed for the numerical solution of initial value problems of second-order ordinary differential equations. The proposed methods are symmetric and belongs to the family of multiderivative methods. Each methods of the new family appears to be hybrid, but after implementing the hybrid terms, it will continue as a multiderivative method. Therefore, the name semi-hybrid is used. The consistency, convergence, stability and periodicity of the methods are investigated and analyzed. The numerical results for some chemical (e.g. undamped Dufng's equation) as well as quantum chemistry problems (i.e. orbit problems of Stiefel and Bettis) indicated that the new method is superior, efcient, accurate and stable.
{"title":"A new two-step hybrid singularly P-stable method for the numerical solution of second-order IVPs with oscillating solutions","authors":"A. Shokri, M. M. Khalsaraei, Ali Atashyar","doi":"10.22052/IJMC.2020.224324.1493","DOIUrl":"https://doi.org/10.22052/IJMC.2020.224324.1493","url":null,"abstract":"In this paper, a new two-step hybrid method of twelfth algebraic order is constructed and analyzed for the numerical solution of initial value problems of second-order ordinary differential equations. The proposed methods are symmetric and belongs to the family of multiderivative methods. Each methods of the new family appears to be hybrid, but after implementing the hybrid terms, it will continue as a multiderivative method. Therefore, the name semi-hybrid is used. The consistency, convergence, stability and periodicity of the methods are investigated and analyzed. The numerical results for some chemical (e.g. undamped Duf\u0002ng's equation) as well as quantum chemistry problems (i.e. orbit problems of Stiefel and Bettis) indicated that the new method is superior, ef\u0002cient, accurate and stable.","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":"79511921","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.2020.221182.1488
Hahder Shelash, Ali A. Shukur
Let G be a simple graph of order N, the concept of resol-vent energy of graph G; i.e. ER(G)=sum_{i=1}^N (N - λi)^{-1} was established in Resolvent Energy of Graphs, MATCH commun. Math. comput. chem., 75 (2016), 279-290. In this paper we study the set of resol-vents energies of graph G which it is called pseudospectrum energy of graph PS(G). For large value resolvent energy of graph ER(G) and real eigenvalues, we establish a number of properties of PS(G): For complex eigenvalues, some examples of PS(G) are given.
{"title":"Pseudospectrum Energy of Graphs","authors":"Hahder Shelash, Ali A. Shukur","doi":"10.22052/IJMC.2020.221182.1488","DOIUrl":"https://doi.org/10.22052/IJMC.2020.221182.1488","url":null,"abstract":"Let G be a simple graph of order N, the concept of resol-vent energy of graph G; i.e. ER(G)=sum_{i=1}^N (N - λi)^{-1} was established in Resolvent Energy of Graphs, MATCH commun. Math. comput. chem., 75 (2016), 279-290. In this paper we study the set of resol-vents energies of graph G which it is called pseudospectrum energy of graph PS(G). For large value resolvent energy of graph ER(G) and real eigenvalues, we establish a number of properties of PS(G): For complex eigenvalues, some examples of PS(G) are given.","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":"88645296","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.2020.224280.1492
Emeric Deutsch, S. Klavžar
Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices of degrees $2$ and $3$ is given that involves only invariants related to the degree $2$ vertices and the number of faces. The approach is applied on several families of chemical graphs. In one of these families an error from the literature is corrected.
{"title":"On the M-polynomial of planar chemical graphs","authors":"Emeric Deutsch, S. Klavžar","doi":"10.22052/IJMC.2020.224280.1492","DOIUrl":"https://doi.org/10.22052/IJMC.2020.224280.1492","url":null,"abstract":"Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices of degrees $2$ and $3$ is given that involves only invariants related to the degree $2$ vertices and the number of faces. The approach is applied on several families of chemical graphs. In one of these families an error from the literature is corrected.","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":"83015781","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.2019.160538.1414
R. Modabernia
Let GF(q) denote the finite field with q elements. The Paley graph Paley(q) is defined to be a graph with vertex set GF(q) such that two vertices a and b are joined with an edge if a-b is a non-zero square. If we assume q≡1(mod4) , then this graph is undirected. In this paper, our aim is to compute the topological indices of Paley(q) such as the Wiener, PI and Szeged indices of this graph.
{"title":"Some Topological Indices Related to Paley Graphs","authors":"R. Modabernia","doi":"10.22052/IJMC.2019.160538.1414","DOIUrl":"https://doi.org/10.22052/IJMC.2019.160538.1414","url":null,"abstract":"Let GF(q) denote the finite field with q elements. The Paley graph Paley(q) is defined to be a graph with vertex set GF(q) such that two vertices a and b are joined with an edge if a-b is a non-zero square. If we assume q≡1(mod4) , then this graph is undirected. In this paper, our aim is to compute the topological indices of Paley(q) such as the Wiener, PI and Szeged indices of this graph.","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":"72473101","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.2020.221320.1489
Hechao Liu, Ling Song, Qiqi Xiao, Zikai Tang
The edge Mostar index 𝑀𝑜𝑒(𝐺) of a connected graph 𝐺 is defined as 𝑀𝑜𝑒(𝐺)=Σ𝑒=𝑢𝑣∈𝐸(𝐺) |𝑚𝑢(𝑒|𝐺)−𝑚𝑣(𝑒|𝐺)|, where 𝑚𝑢(𝑒|𝐺)and 𝑚𝑣(𝑒|𝐺) are, respectively, the number of edges of 𝐺 lying closer to vertex 𝑢 than to vertex 𝑣 and the number of edges of 𝐺 lying closer to vertex 𝑣 than to vertex 𝑢. In this paper, we determine the extremal values of edge Mostar index of some graphs. We characterize extremal trees, unicyclic graphs and determine the extremal graphs with maximum and second maximum edge Mostar index among cacti with size 𝑚 and 𝑡 cycles. At last, we give some open problems.
{"title":"On edge Mostar index of graphs","authors":"Hechao Liu, Ling Song, Qiqi Xiao, Zikai Tang","doi":"10.22052/IJMC.2020.221320.1489","DOIUrl":"https://doi.org/10.22052/IJMC.2020.221320.1489","url":null,"abstract":"The edge Mostar index 𝑀𝑜𝑒(𝐺) of a connected graph 𝐺 is defined as 𝑀𝑜𝑒(𝐺)=Σ𝑒=𝑢𝑣∈𝐸(𝐺) |𝑚𝑢(𝑒|𝐺)−𝑚𝑣(𝑒|𝐺)|, where 𝑚𝑢(𝑒|𝐺)and 𝑚𝑣(𝑒|𝐺) are, respectively, the number of edges of 𝐺 lying closer to vertex 𝑢 than to vertex 𝑣 and the number of edges of 𝐺 lying closer to vertex 𝑣 than to vertex 𝑢. In this paper, we determine the extremal values of edge Mostar index of some graphs. We characterize extremal trees, unicyclic graphs and determine the extremal graphs with maximum and second maximum edge Mostar index among cacti with size 𝑚 and 𝑡 cycles. At last, we give some open problems.","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":"90886413","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 : 2020-03-01DOI: 10.22052/IJMC.2020.174205.1429
N. Karamzadeh, M. Darafsheh
The n-star graph Sn is defined on the set of all n sequenses (u1,u2,...,un), ui ∈ {1, 2, ..., n}, ui ne uj and i ne j, where edges are of the form (u1,u2,...,un) ∼ (ui,u2,...,un), for some i ne 1. In this paper we will show that Sn is a vertex and edge transitive graph and discuss some topological properties of Sn.
n星图Sn定义在所有n个序列(u1,u2，…，un)的集合上，ui∈{1,2，…， n}， UI ne uj和I ne j，其中边的形式为(u1,u2，…，un) ~ (UI,u2，…，un)，对于某些I ne 1。本文证明了Sn是一个点边传递图，并讨论了Sn的一些拓扑性质。
{"title":"On Topological Properties of the n-Star Graph","authors":"N. Karamzadeh, M. Darafsheh","doi":"10.22052/IJMC.2020.174205.1429","DOIUrl":"https://doi.org/10.22052/IJMC.2020.174205.1429","url":null,"abstract":"The n-star graph Sn is defined on the set of all n sequenses (u1,u2,...,un), ui ∈ {1, 2, ..., n}, ui ne uj and i ne j, where edges are of the form (u1,u2,...,un) ∼ (ui,u2,...,un), for some i ne 1. In this paper we will show that Sn is a vertex and edge transitive graph and discuss some topological properties of Sn.","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":"73674177","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 : 2020-03-01DOI: 10.22052/IJMC.2020.148532.1390
Risong Li
In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itself is said to be P-chaotic if it has the pseudo-orbit-tracing property and the closure of the set of all periodic points for $Theta$ is the space $Z$. Also, an example and three open problems are presented.
{"title":"Kato's chaos and P-chaos of a coupled lattice system given by Garcia Guirao and Lampart which is related with Belusov-Zhabotinskii reaction","authors":"Risong Li","doi":"10.22052/IJMC.2020.148532.1390","DOIUrl":"https://doi.org/10.22052/IJMC.2020.148532.1390","url":null,"abstract":"In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itself is said to be P-chaotic if it has the pseudo-orbit-tracing property and the closure of the set of all periodic points for $Theta$ is the space $Z$. Also, an example and three open problems are presented.","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":"72422872","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 : 2020-03-01DOI: 10.22052/IJMC.2020.207671.1472
M. M. Khalsaraei, A. Shokri
In this paper, we introduce a new symmetric explicit four-step method with variable coefficients for the numerical solution of second-order linear periodic and oscillatory initial value problems of ordinary differential equations. For the first time in the literature, we generate an explicit method with the most important singularly P-stability property. The method is multiderivative and has algebraic order eight and infinite order of phase-lag. The numerical results for some chemical (e.g. orbit problems of Stiefel and Bettis) as well as quantum chemistry problems (i.e. systems of coupled differential equations) indicated that the new method is superior, efficient, accurate and stable.
{"title":"A New Explicit Singularly P-Stable Four-Step Method for the Numerical Solution of Second Order IVPs","authors":"M. M. Khalsaraei, A. Shokri","doi":"10.22052/IJMC.2020.207671.1472","DOIUrl":"https://doi.org/10.22052/IJMC.2020.207671.1472","url":null,"abstract":"In this paper, we introduce a new symmetric explicit four-step method with variable coefficients for the numerical solution of second-order linear periodic and oscillatory initial value problems of ordinary differential equations. For the first time in the literature, we generate an explicit method with the most important singularly P-stability property. The method is multiderivative and has algebraic order eight and infinite order of phase-lag. The numerical results for some chemical (e.g. orbit problems of Stiefel and Bettis) as well as quantum chemistry problems (i.e. systems of coupled differential equations) indicated that the new method is superior, efficient, accurate and stable.","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":"78675545","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 : 2020-03-01DOI: 10.22052/IJMC.2020.215860.1480
T. Došlić
We present explicit formulas for the Laplacian Szeged eigenvalues of paths, grids, $C_4$-nanotubes and of Cartesian products of paths with some other simple graphs. A number of open problems is listed.
{"title":"On the Laplacian Szeged spectrum of paths","authors":"T. Došlić","doi":"10.22052/IJMC.2020.215860.1480","DOIUrl":"https://doi.org/10.22052/IJMC.2020.215860.1480","url":null,"abstract":"We present explicit formulas for the Laplacian Szeged eigenvalues of paths, grids, $C_4$-nanotubes and of Cartesian products of paths with some other simple graphs. A number of open problems is listed.","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":"86063543","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 : 2020-03-01DOI: 10.22052/IJMC.2020.209321.1475
M. Ghorbani, Shaghayegh Rahmani, Mohammad Eslampoor
A general bond additive index (GBA) can be defined as , where α(e) is edge contributions. The Mostar index is a new topological index whose edge contributions are α(e) = | nu - nv| in which nu is the number of vertices of lying closer to vertex u than to vertex v and nv can be defined similarly. In this paper, we propose some new results on the Mostar index based on the vertex-orbits under the action of automorphism group. In addition, we detrmined the structures of graphs with Mostar index equal 1. Finally, compute the Mostar index of a family of nanocone graphs.
一般的键加性指数(GBA)可以定义为，其中α(e)是边贡献。Mostar指标是一种新的拓扑指标，它的边贡献为α(e) = | nu - nv|，其中nu是靠近顶点u而不是靠近顶点v的顶点数，nv可以类似地定义。本文给出了自同构群作用下基于顶点轨道的Mostar指数的一些新结果。此外，我们还确定了Mostar指数为1的图的结构。最后，计算了一类纳米锥图的Mostar指数。
{"title":"Some New Results on Mostar Index of Graphs","authors":"M. Ghorbani, Shaghayegh Rahmani, Mohammad Eslampoor","doi":"10.22052/IJMC.2020.209321.1475","DOIUrl":"https://doi.org/10.22052/IJMC.2020.209321.1475","url":null,"abstract":"A general bond additive index (GBA) can be defined as , where α(e) is edge contributions. The Mostar index is a new topological index whose edge contributions are α(e) = | nu - nv| in which nu is the number of vertices of lying closer to vertex u than to vertex v and nv can be defined similarly. In this paper, we propose some new results on the Mostar index based on the vertex-orbits under the action of automorphism group. In addition, we detrmined the structures of graphs with Mostar index equal 1. Finally, compute the Mostar index of a family of nanocone graphs.","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":"82911131","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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