Pub Date : 2022-08-01DOI: 10.46793/match.89-2.405y
Jingzhi Yan, Feng Guan
The degree-based graph entropy Id is a parametric measure derived from an information functional defined by vertex degrees of a graph, which is used to characterize the structure of complex networks. Determining minimal values of Id is challenging due to a lack of effective methods to analyze properties of minimal graphs. In this paper, we investigate minimal properties of the graph entropy in (n, m)-graphs and define two new graph operations, which can decrease the values of Id.
{"title":"Graph Operations Decreasing Values of Degree-Based Graph Entropies","authors":"Jingzhi Yan, Feng Guan","doi":"10.46793/match.89-2.405y","DOIUrl":"https://doi.org/10.46793/match.89-2.405y","url":null,"abstract":"The degree-based graph entropy Id is a parametric measure derived from an information functional defined by vertex degrees of a graph, which is used to characterize the structure of complex networks. Determining minimal values of Id is challenging due to a lack of effective methods to analyze properties of minimal graphs. In this paper, we investigate minimal properties of the graph entropy in (n, m)-graphs and define two new graph operations, which can decrease the values of Id.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"176 12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72534653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-1.143l
Zuozhi Liu
Establishing suitable differential dynamical models to describe the real natural phenomenon in chemistry and physics has become a very hot topic in nowadays society. In this present research, we deal with a fractional-order chemical reaction system. Taking advantage of the fixed point theorem, we prove the existence and uniqueness of the fractional-order chemical reaction system. Using the inequality skill, we prove the non-negativeness of the fractional-order chemical reaction system. By applying a suitable function, we prove the uniform boundedness of the solution to the fractional-order chemical reaction system. With the aid of a hybrid controller including state feedback and parameter perturbation, we discuss the Hopf bifurcation anti-control issue of the fractional-order stable chemical reaction system. A novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation of the involved fractional-order stable chemical reaction system is set up. The study manifests that the delay in the hybrid controller plays a vital role in stabilizing the system and controlling the occurrence of Hopf bifurcation of the fractional-order stable chemical reaction system. In order to validate the derived key conclusions, MATLAB simulations are executed and bifurcation plots are given. The obtained results of this article have momentous theoretical guiding value in controlling the chemical compositions. The exploration idea can also be utilized to investigate the bifurcation control and bifurcation anti-control problems in lots of other fractional-order differential systems in numerous disciplines.
{"title":"Bifurcation Anti-Control Tactics of a Fractional-Order Stable Chemical Reaction System","authors":"Zuozhi Liu","doi":"10.46793/match.89-1.143l","DOIUrl":"https://doi.org/10.46793/match.89-1.143l","url":null,"abstract":"Establishing suitable differential dynamical models to describe the real natural phenomenon in chemistry and physics has become a very hot topic in nowadays society. In this present research, we deal with a fractional-order chemical reaction system. Taking advantage of the fixed point theorem, we prove the existence and uniqueness of the fractional-order chemical reaction system. Using the inequality skill, we prove the non-negativeness of the fractional-order chemical reaction system. By applying a suitable function, we prove the uniform boundedness of the solution to the fractional-order chemical reaction system. With the aid of a hybrid controller including state feedback and parameter perturbation, we discuss the Hopf bifurcation anti-control issue of the fractional-order stable chemical reaction system. A novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation of the involved fractional-order stable chemical reaction system is set up. The study manifests that the delay in the hybrid controller plays a vital role in stabilizing the system and controlling the occurrence of Hopf bifurcation of the fractional-order stable chemical reaction system. In order to validate the derived key conclusions, MATLAB simulations are executed and bifurcation plots are given. The obtained results of this article have momentous theoretical guiding value in controlling the chemical compositions. The exploration idea can also be utilized to investigate the bifurcation control and bifurcation anti-control problems in lots of other fractional-order differential systems in numerous disciplines.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"33 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88434282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-2.517f
S. Filipovski
Based on computer search, Furtula characterized the connected graphs with maximal ABCGG index. In this paper we give a mathematical proof of the established hypothesizes.
{"title":"Connected Graphs with Maximal Graovac-Ghorbani Index","authors":"S. Filipovski","doi":"10.46793/match.89-2.517f","DOIUrl":"https://doi.org/10.46793/match.89-2.517f","url":null,"abstract":"Based on computer search, Furtula characterized the connected graphs with maximal ABCGG index. In this paper we give a mathematical proof of the established hypothesizes.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"92 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82383639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-2.415l
Hechao Liu, L. You, Yufei Huang, Zikai Tang
{"title":"On Extremal Sombor Indices of Chemical Graphs, and Beyond","authors":"Hechao Liu, L. You, Yufei Huang, Zikai Tang","doi":"10.46793/match.89-2.415l","DOIUrl":"https://doi.org/10.46793/match.89-2.415l","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"32 2 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88198257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-2.275d
Emeric Deutsch, S. Klavžar, Gašper Domen Romih
Let G be a graph and let m i,j ( G ), i, j ≥ 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 ) = (cid:80) i ≤ j m i,j ( G ) x i y j . A general method for calculating the M-polynomials for arbitrary graph families is presented. The method is further developed for the case where the vertices of a graph have degrees 2 and p , where p ≥ 3, and further for such planar graphs. The method is illustrated on families of chemical graphs.
设G是一个图，m i,j (G)， i,j≥1，为G的边数uv，使{d v (G)， d u (G)} = {i,j}。G的M多项式是M (G;x, y) = (cid:80) i≤j m i,j (G) x i y j。给出了计算任意图族m多项式的一般方法。对于图的顶点具有2度和p度，且p≥3的情况，以及此类平面图，进一步发展了该方法。用化学图族说明了这种方法。
{"title":"How to Compute the M-Polynomial of (Chemical) Graphs","authors":"Emeric Deutsch, S. Klavžar, Gašper Domen Romih","doi":"10.46793/match.89-2.275d","DOIUrl":"https://doi.org/10.46793/match.89-2.275d","url":null,"abstract":"Let G be a graph and let m i,j ( G ), i, j ≥ 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 ) = (cid:80) i ≤ j m i,j ( G ) x i y j . A general method for calculating the M-polynomials for arbitrary graph families is presented. The method is further developed for the case where the vertices of a graph have degrees 2 and p , where p ≥ 3, and further for such planar graphs. The method is illustrated on families of chemical graphs.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"39 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89474207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The traditional method to improve the yield of Buchwald-Hartwig cross coupling reaction is to change the reactants or reaction conditions, but the reaction has many problems, such as harsh reaction conditions, complex synthetic route. In 2018, Doyle reported a yield prediction method based on random forest in Science. However, the predicted value of the regression tree in the random forest is the average value of the target variable of the leaf node, which treats the feature as equally important. We focused on the important characteristic information in order to obtain a more accurate yield prediction value. Therefore, it is of interest to apply some advanced deep learning methods to the performance prediction of chemical reactions, during which less training data may be required.
{"title":"Regression Prediction of Coupling Reaction Yield Based on Attention-Driven Convolutional Neural Network","authors":"Hexun Hou, Hengzhe Wang, Yanhui Guo, Puyu Zhang, Lichao Peng, Xiaohui Yang","doi":"10.46793/match.89-1.199h","DOIUrl":"https://doi.org/10.46793/match.89-1.199h","url":null,"abstract":"The traditional method to improve the yield of Buchwald-Hartwig cross coupling reaction is to change the reactants or reaction conditions, but the reaction has many problems, such as harsh reaction conditions, complex synthetic route. In 2018, Doyle reported a yield prediction method based on random forest in Science. However, the predicted value of the regression tree in the random forest is the average value of the target variable of the leaf node, which treats the feature as equally important. We focused on the important characteristic information in order to obtain a more accurate yield prediction value. Therefore, it is of interest to apply some advanced deep learning methods to the performance prediction of chemical reactions, during which less training data may be required.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"65 19","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72494251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-2.287n
R. M. Nemba
{"title":"Vector Spaces of Permutomers and Symmetry Itemized Isomers Numbers for Substituted C2v-Based Compounds. I","authors":"R. M. Nemba","doi":"10.46793/match.89-2.287n","DOIUrl":"https://doi.org/10.46793/match.89-2.287n","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"27 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83572866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-2.503s
Zhenhua Su, Zikai Tang, H. Deng
{"title":"Extremal Wiener Index of Graphs with Given Number of Vertices of Odd Degree","authors":"Zhenhua Su, Zikai Tang, H. Deng","doi":"10.46793/match.89-2.503s","DOIUrl":"https://doi.org/10.46793/match.89-2.503s","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"88 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90536371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-2.479j
Irena M. Jovanović, E. Zogic, E. Glogic
Let Gσ be a graph obtained by attaching a self-loop, or just a loop, for short, at each of σ chosen vertices of a given graph G. Gutman et al. have recently introduced the concept of the energy of graphs with self-loops, and conjectured that the energy E(G) of a graph G of order n is always strictly less than the energy E(Gσ) of a corresponding graph Gσ, for 1 ≤ σ ≤ n − 1. In this paper, a simple set of graphs which disproves this conjecture is exposed, together with some remarks regarding the standard deviations of the (adjacency) eigenvalues of G and Gσ, respectively.
{"title":"On the Conjecture Related to the Energy of Graphs with Self–Loops","authors":"Irena M. Jovanović, E. Zogic, E. Glogic","doi":"10.46793/match.89-2.479j","DOIUrl":"https://doi.org/10.46793/match.89-2.479j","url":null,"abstract":"Let Gσ be a graph obtained by attaching a self-loop, or just a loop, for short, at each of σ chosen vertices of a given graph G. Gutman et al. have recently introduced the concept of the energy of graphs with self-loops, and conjectured that the energy E(G) of a graph G of order n is always strictly less than the energy E(Gσ) of a corresponding graph Gσ, for 1 ≤ σ ≤ n − 1. In this paper, a simple set of graphs which disproves this conjecture is exposed, together with some remarks regarding the standard deviations of the (adjacency) eigenvalues of G and Gσ, respectively.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74772844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.46793/match.89-2.327g
S. Gong, Liping Zhang, Changbao Su
Let G be a simple graph with order n , n ≥ 5, and adjacency matrix A ( G ). In this paper, we determine the number of all substructures having at most four edges in terms of its adjacency matrix A ( G ) together with some graph invariants determined by A ( G ). Then, as applications, we provide an algebraic expression for the second Zagreb index and || A 4 || of a graph.
{"title":"On the Number of All Substructures Containing at Most Four Edges","authors":"S. Gong, Liping Zhang, Changbao Su","doi":"10.46793/match.89-2.327g","DOIUrl":"https://doi.org/10.46793/match.89-2.327g","url":null,"abstract":"Let G be a simple graph with order n , n ≥ 5, and adjacency matrix A ( G ). In this paper, we determine the number of all substructures having at most four edges in terms of its adjacency matrix A ( G ) together with some graph invariants determined by A ( G ). Then, as applications, we provide an algebraic expression for the second Zagreb index and || A 4 || of a graph.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"54 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81558796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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