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Iranian journal of mathematical chemistry最新文献

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On the trees with given matching number and the modified first Zagreb connection index 给定匹配数和修改后的第一个萨格勒布连接索引的树
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-09-01 DOI: 10.22052/IJMC.2021.242169.1554
Sadia Noureen, A. A. Bhatti
{"title":"On the trees with given matching number and the modified first Zagreb connection index","authors":"Sadia Noureen, A. A. Bhatti","doi":"10.22052/IJMC.2021.242169.1554","DOIUrl":"https://doi.org/10.22052/IJMC.2021.242169.1554","url":null,"abstract":"The modified first Zagreb connection index ZC∗1 for a graph G is defined as ZC∗1 (G) = sum v∈V (G) dvτv , where dv is the degree of the vertex v and τv denotes the connection number of v (that is, the number of vertices at the distance 2 from the vertex v). Let Tn,α be the class of trees with order n and matching number α such that n > 2α−1. In this paper, we obtain the lower bounds on the modified first Zagreb connection index of trees belonging to the class Tn,α, for 2α − 1 < n < 3α + 2.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89019895","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}
引用次数: 1
Upper and Lower Bounds for the First and Second Zagreb Indices of Quasi Bicyclic Graphs 拟双环图的第一和第二Zagreb指标的上界和下界
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-06-01 DOI: 10.22052/IJMC.2021.202592.1466
Majid Aghel, A. Erfanian, T. Dehghan-Zadeh
{"title":"Upper and Lower Bounds for the First and Second Zagreb Indices of Quasi Bicyclic Graphs","authors":"Majid Aghel, A. Erfanian, T. Dehghan-Zadeh","doi":"10.22052/IJMC.2021.202592.1466","DOIUrl":"https://doi.org/10.22052/IJMC.2021.202592.1466","url":null,"abstract":"The aim of this paper is to give an upper and lower bounds for the first and second Zagreb indices of quasi bicyclic graphs. For a simple graph G, we denote M1(G) and M2(G), as the sum of deg2(u) overall vertices u in G and the sum of deg(u)deg(v) of all edges uv of G, respectively. The graph G is called quasi bicyclic graph if there exists a vertex x ∈ V (G) such that G−x is a connected bicyclic graph. The results mentioned in this paper, are mostly new or an improvement of results given by authors for quasi unicyclic graphs in [1].","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75965071","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}
引用次数: 0
On the Characteristic Polynomial and Spectrum of the Terminal Distance Matrix of Kragujevac Trees Kragujevac树终端距离矩阵的特征多项式和谱
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-06-01 DOI: 10.22052/IJMC.2021.242219.1559
A. Heydari
{"title":"On the Characteristic Polynomial and Spectrum of the Terminal Distance Matrix of Kragujevac Trees","authors":"A. Heydari","doi":"10.22052/IJMC.2021.242219.1559","DOIUrl":"https://doi.org/10.22052/IJMC.2021.242219.1559","url":null,"abstract":"In this paper‎, ‎the characteristic polynomial and the spectrum of the terminal distance matrix for some Kragujevac trees is computed. ‎As Application‎, ‎we obtain an upper bound and a lower bound for the spectral radius of the terminal distance matrix of the Kragujevac trees‎.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88248020","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}
引用次数: 0
Steiner Wiener Index of Complete m-Ary Trees 完全m-Ary树的Steiner Wiener索引
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-06-01 DOI: 10.22052/IJMC.2021.242136.1552
Mesfin Masre Legese
{"title":"Steiner Wiener Index of Complete m-Ary Trees","authors":"Mesfin Masre Legese","doi":"10.22052/IJMC.2021.242136.1552","DOIUrl":"https://doi.org/10.22052/IJMC.2021.242136.1552","url":null,"abstract":"Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. For a subset $S$ of $V(G)$, the Steiner distance $d(S)$ of $S$ is the minimum size of a connected subgraph whose vertex set contains $S$. For an integer $k$ with $2 le k le n - 1$, the $k$-th Steiner Wiener index of a graph $G$ is defined as $SW_k(G) = sum_{substack{Ssubseteq V(G) |S|=k}}d(S)$. In this paper, we present exact values of the $k$-th Steiner Wiener index of complete $m$-ary trees by using inclusion-excluision principle for various values of $k$.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78028112","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}
引用次数: 0
The Gutman Index and Schultz Index in the Random Phenylene Chains 随机苯基链中的Gutman指数和Schultz指数
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-06-01 DOI: 10.22052/IJMC.2021.240317.1527
Lina Wei, H. Bian, Haizheng Yu, Xiaoying Yang
{"title":"The Gutman Index and Schultz Index in the Random Phenylene Chains","authors":"Lina Wei, H. Bian, Haizheng Yu, Xiaoying Yang","doi":"10.22052/IJMC.2021.240317.1527","DOIUrl":"https://doi.org/10.22052/IJMC.2021.240317.1527","url":null,"abstract":"The Gutman index and Schultz index are two topological indices‎. ‎In this paper‎, ‎we first give exact formulae for the expected values of the Gutman index and Schultz index of random phenylene chains‎, ‎and we will also get the average values of the Gutman index and Schultz index in phenylene chains.‎","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77147607","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}
引用次数: 1
A new notion of energy of digraphs 有向图能量的新概念
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-06-01 DOI: 10.22052/IJMC.2020.224853.1496
Mehtab Khan
{"title":"A new notion of energy of digraphs","authors":"Mehtab Khan","doi":"10.22052/IJMC.2020.224853.1496","DOIUrl":"https://doi.org/10.22052/IJMC.2020.224853.1496","url":null,"abstract":"The eigenvalues of a digraph are the eigenvalues of its adjacency matrix. Let $z_1,ldots,z_n$ be the eigenvalues of an $n$-vertex digraph $D$. Then we give a new notion of energy of digraphs defined by $E_p(D)=sum_{k=1}^{n}|{Re}(z_k) {Im}(z_k)|$, where ${Re}(z_k)$ (respectively, ${Im}(z_k)$) is real (respectively, imaginary) part of $z_k$. We call it $p$-energy of the digraph $D$. We compute $p$-energy formulas for directed cycles. For $ngeq 12$, we show that $p$-energy of directed cycles increases monotonically with respect to their order. We find unicyclic digraphs with smallest and largest $p$-energy. We give counter examples to show that the $p$-energy of digraph does not possess increasing--property with respect to quasi-order relation over the set $mathcal{D}_{n,h}$, where $mathcal{D}_{n,h}$ is the set of $n$-vertex digraphs with cycles of length $h$. We find the upper bound for $p$-energy and give all those digraphs which attain this bound. Moreover, we construct few families of $p$-equienergetic digraphs.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76029341","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}
引用次数: 2
Topological Entropy, Distributional Chaos and the Principal Measure of a Class of Belusov−Zhabotinskii's Reaction Models Presented by García Guirao and Lampart García Guirao和Lampart提出的一类Belusov - Zhabotinskii反应模型的拓扑熵、分布混沌和主测度
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-03-01 DOI: 10.22052/IJMC.2021.240450.1541
Hongqing Wang, Risong Li
{"title":"Topological Entropy, Distributional Chaos and the Principal Measure of a Class of Belusov−Zhabotinskii's Reaction Models Presented by García Guirao and Lampart","authors":"Hongqing Wang, Risong Li","doi":"10.22052/IJMC.2021.240450.1541","DOIUrl":"https://doi.org/10.22052/IJMC.2021.240450.1541","url":null,"abstract":"In this paper‎, ‎the chaotic properties of‎ ‎the following Belusov-Zhabotinskii's reaction model is explored:‎ ‎alk+1=(1-η)θ(‎alk)+(1/2) η[θ(‎al-1k)-θ(al+1k)], where k is discrete‎ ‎time index‎, ‎l is lattice side index with system size M‎, η∊ ‎[0‎, ‎1) is coupling constant and $theta$ is a continuous map on‎ ‎W=[-1‎, ‎1]. This kind of system is a generalization of the chemical‎ ‎reaction model which was presented by Garcia Guirao and Lampart‎ ‎in [Chaos of a coupled lattice system related with the Belusov–Zhabotinskii reaction, J. Math. Chem. ‎48 (2010) 159-164] and stated by Kaneko in [Globally coupled chaos violates the law of large numbers but not the central-limit theorem, Phys. Rev.‎ ‎Lett‎. ‎65‎ (1990) ‎1391-1394]‎, ‎and it is closely related to the‎ ‎Belusov-Zhabotinskii's reaction‎. ‎In particular‎, ‎it is shown that for‎ ‎any coupling constant η ∊ [0‎, ‎1/2)‎, ‎any‎ ‎r ∊ {1‎, ‎2‎, ...} and θ=Qr‎, ‎the topological entropy‎ ‎of this system is greater than or equal to rlog(2-2η)‎, ‎and‎ ‎that this system is Li-Yorke chaotic and distributionally chaotic,‎ ‎where the map Q is defined by‎ ‎Q(a)=1-|1-2a|‎, ‎ a ∊ [0‎, ‎1], and Q(a)=-Q(-a),‎ a ∊ [-1‎, ‎0]. Moreover‎, ‎we also show that for any c‎, ‎d with‎ ‎0≤c≤ d≤ 1, ‎η=0 and θ=Q‎, ‎this system is‎ ‎distributionally (c‎, ‎d)-chaotic.‎","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73161154","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}
引用次数: 0
Relations between Sombor Index and some Degree-Based Topological Indices Sombor指数与一些基于度的拓扑指数的关系
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-03-01 DOI: 10.22052/IJMC.2021.240385.1533
S. Filipovski
{"title":"Relations between Sombor Index and some Degree-Based Topological Indices","authors":"S. Filipovski","doi":"10.22052/IJMC.2021.240385.1533","DOIUrl":"https://doi.org/10.22052/IJMC.2021.240385.1533","url":null,"abstract":"In [13] Gutman introduced a novel graph invariant called Sombor index SO, defined via $sqrt{deg(u)^{2}+deg(v)^{2}}.$ In this paper we provide relations between Sombor index and some degree-based topological indices: Zagreb indices, Forgotten index and Randi' {c} index. Similar relations are established in the class of triangle-free graphs.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86696990","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}
引用次数: 14
Sombor index of certain graphs 某些图的Sombor指数
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2021-02-20 DOI: 10.22052/IJMC.2021.242106.1547
Nima Ghanbari, S. Alikhani
{"title":"Sombor index of certain graphs","authors":"Nima Ghanbari, S. Alikhani","doi":"10.22052/IJMC.2021.242106.1547","DOIUrl":"https://doi.org/10.22052/IJMC.2021.242106.1547","url":null,"abstract":"Let $G=(V,E)$ be a finite simple graph. The Sombor index $SO(G)$ of $G$ is defined as $sum_{uvin E(G)}sqrt{d_u^2+d_v^2}$, where $d_u$ is the degree of vertex $u$ in $G$. In this paper, we study this index for certain graphs and we examine the effects on $SO(G)$ when $G$ is modified by operations on vertex and edge of $G$. Also we present bounds for the Sombor index of join and corona product of two graphs.","PeriodicalId":14545,"journal":{"name":"Iranian journal of mathematical chemistry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2021-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86558564","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}
引用次数: 17
The Expected Values of Merrifield-Simmons Index in Random Phenylene Chains 随机苯基链的Merrifield-Simmons指数期望值
IF 1.3
Iranian journal of mathematical chemistry Pub Date : 2020-12-01 DOI: 10.22052/IJMC.2020.237192.1508
Lina Wei, H. Bian, Haizheng Yu, Jili Ding
{"title":"The Expected Values of Merrifield-Simmons Index in Random Phenylene Chains","authors":"Lina Wei, H. Bian, Haizheng Yu, Jili Ding","doi":"10.22052/IJMC.2020.237192.1508","DOIUrl":"https://doi.org/10.22052/IJMC.2020.237192.1508","url":null,"abstract":"The Merrifield-Simmons index of a graph G is the number of independent sets in G. In this paper, we give exact formulae for the expected value of the Merrifield-Simmons index of random phenylene chains by means of auxiliary graphs.","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":"79130987","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}
引用次数: 2
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