Pub Date : 2023-01-01DOI: 10.46793/match.89-3.741z
Mengyue Zhang, Biao Zhao
{"title":"Extremal Values of the Sombor Index in Tricyclic Graphs","authors":"Mengyue Zhang, Biao Zhao","doi":"10.46793/match.89-3.741z","DOIUrl":"https://doi.org/10.46793/match.89-3.741z","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86653090","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 : 2023-01-01DOI: 10.46793/match.89-3.631p
R. Poojary, A. Bhat K, M. Karantha, S. Arumugam, I. Gutman
The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of G. A unified approach is presented for the characterization of graphs of order n with η(G) = n−4. All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and r-partite graphs, for which η(G) = n−4 are shown to be corollaries of a theorem of Chang, Huang and Yeh that characterizes all graphs with nullity n − 4.
{"title":"Characterizing Graphs with Nullity n-4","authors":"R. Poojary, A. Bhat K, M. Karantha, S. Arumugam, I. Gutman","doi":"10.46793/match.89-3.631p","DOIUrl":"https://doi.org/10.46793/match.89-3.631p","url":null,"abstract":"The nullity of a graph G, denoted by η(G), is the multiplicity of the eigenvalue zero in the spectrum of G. A unified approach is presented for the characterization of graphs of order n with η(G) = n−4. All known results on trees, unicyclic graphs, bicyclic graphs, graphs with minimum degree 1, and r-partite graphs, for which η(G) = n−4 are shown to be corollaries of a theorem of Chang, Huang and Yeh that characterizes all graphs with nullity n − 4.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87406322","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 : 2023-01-01DOI: 10.46793/match.89-3.653a
S. Akbari, Hamideh Alizadeh, M. Fakharan, M. Habibi, Samane Rabizadeh, Soheyr Rouhani
In this paper, we extend some results of [F. Shaveisi, lower bounds on the vertex cover number and energy of graphs, MATCH Commun. Math. Comput. Chem, 87(3) (2022) 683-692] which state some relations between the vertex cover and other parameters, such as the order and maximum or minimum degree of graphs. Also, we prove that for a graph G, E(G) ≥ 2β(G)−2Ce(G) and so E(G) ≥ 2β(G) − 2C(G), where E(G), β(G), Ce(G) and C(G) denote the energy, vertex cover, number of even cycles and number of cycles in G, respectively. For these both inequalities we investigate their equality. Finally, we give some relations between E(G),γ(G) and γt(G), where γ(G) and γt(G) are domination number and total domination number of G, respectively.
{"title":"Some Relations Between Rank, Vertex Cover Number and Energy of Graph","authors":"S. Akbari, Hamideh Alizadeh, M. Fakharan, M. Habibi, Samane Rabizadeh, Soheyr Rouhani","doi":"10.46793/match.89-3.653a","DOIUrl":"https://doi.org/10.46793/match.89-3.653a","url":null,"abstract":"In this paper, we extend some results of [F. Shaveisi, lower bounds on the vertex cover number and energy of graphs, MATCH Commun. Math. Comput. Chem, 87(3) (2022) 683-692] which state some relations between the vertex cover and other parameters, such as the order and maximum or minimum degree of graphs. Also, we prove that for a graph G, E(G) ≥ 2β(G)−2Ce(G) and so E(G) ≥ 2β(G) − 2C(G), where E(G), β(G), Ce(G) and C(G) denote the energy, vertex cover, number of even cycles and number of cycles in G, respectively. For these both inequalities we investigate their equality. Finally, we give some relations between E(G),γ(G) and γt(G), where γ(G) and γt(G) are domination number and total domination number of G, respectively.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77805632","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 : 2023-01-01DOI: 10.46793/match.90-1.247v
Deekshitha Vivek Anchan, S. D’souza, H. J. Gowtham, P. G. Bhat
{"title":"Laplacian Energy of a Graph with Self-Loops","authors":"Deekshitha Vivek Anchan, S. D’souza, H. J. Gowtham, P. G. Bhat","doi":"10.46793/match.90-1.247v","DOIUrl":"https://doi.org/10.46793/match.90-1.247v","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75963027","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 : 2023-01-01DOI: 10.46793/match.90-1.175c
X. Cheng, Xueliang Li
This paper gives some bounds for the vertex degree function index Hf(G) in terms of the order and size of a graph G, where G is a simple, finite and connected graph with minimum degree δ and maximum degree ∆. Some families of graphs are also constructed to show that the bounds can be achieved.
{"title":"Some Bounds for the Vertex Degree Function Index of Connected Graphs with Given Minimum and Maximum Degrees","authors":"X. Cheng, Xueliang Li","doi":"10.46793/match.90-1.175c","DOIUrl":"https://doi.org/10.46793/match.90-1.175c","url":null,"abstract":"This paper gives some bounds for the vertex degree function index Hf(G) in terms of the order and size of a graph G, where G is a simple, finite and connected graph with minimum degree δ and maximum degree ∆. Some families of graphs are also constructed to show that the bounds can be achieved.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74041301","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 : 2023-01-01DOI: 10.46793/match.89-3.567c
X. Cheng, Xueliang Li
{"title":"Extremal General Gutman Index of Trees","authors":"X. Cheng, Xueliang Li","doi":"10.46793/match.89-3.567c","DOIUrl":"https://doi.org/10.46793/match.89-3.567c","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75421863","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 : 2023-01-01DOI: 10.46793/match.90-1.053w
Hengzhe Wang, Lichao Peng, Li Chang, Zixin Li, Yanhui Guo, Qian Li, Xiaohui Yang
Machine learning is increasingly popular in predicting chemical reaction performance. This study aims to apply the CatBoost algorithm to build an intelligent prediction system for organic chemical reaction yields. The parameter analysis, convergence analysis, prediction accuracy analysis and generalization analysis are carried out. Then, the internal relationship between reaction conditions and yield is excavated through feature importance and SHAP. The results show that the proposed method has the potential as a high-precision tool to assist the optimization of chemical reaction system.
{"title":"CatBoost-Based Framework for Intelligent Prediction and Reaction Condition Analysis of Coupling Reaction","authors":"Hengzhe Wang, Lichao Peng, Li Chang, Zixin Li, Yanhui Guo, Qian Li, Xiaohui Yang","doi":"10.46793/match.90-1.053w","DOIUrl":"https://doi.org/10.46793/match.90-1.053w","url":null,"abstract":"Machine learning is increasingly popular in predicting chemical reaction performance. This study aims to apply the CatBoost algorithm to build an intelligent prediction system for organic chemical reaction yields. The parameter analysis, convergence analysis, prediction accuracy analysis and generalization analysis are carried out. Then, the internal relationship between reaction conditions and yield is excavated through feature importance and SHAP. The results show that the proposed method has the potential as a high-precision tool to assist the optimization of chemical reaction system.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81674050","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 : 2023-01-01DOI: 10.46793/match.90-1.223h
Amjad E. Hamza, Z. Raza, Akbar Ali, Zainab Alsheekhhussain
This paper indicates alternative ways of deriving the main results of the recent paper [M. Zhang, B. Zhao, Extremal values of the Sombor index in tricyclic graphs, MATCH Commun. Math. Comput. Chem. 89 (2023) 741-758]. The graphs possessing minimum and maximum values of the reduced Sombor index are also characterized from the class of all tricyclic connected graphs of a given order.
{"title":"On Sombor Indices of Tricyclic Graphs","authors":"Amjad E. Hamza, Z. Raza, Akbar Ali, Zainab Alsheekhhussain","doi":"10.46793/match.90-1.223h","DOIUrl":"https://doi.org/10.46793/match.90-1.223h","url":null,"abstract":"This paper indicates alternative ways of deriving the main results of the recent paper [M. Zhang, B. Zhao, Extremal values of the Sombor index in tricyclic graphs, MATCH Commun. Math. Comput. Chem. 89 (2023) 741-758]. The graphs possessing minimum and maximum values of the reduced Sombor index are also characterized from the class of all tricyclic connected graphs of a given order.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83356125","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 : 2023-01-01DOI: 10.46793/match.89-3.529m
D. Mu, Changjin Xu, Zixin Liu, Yicheng Pang
Delayed differential equation is an important tool to describe the interaction of different chemical substance in chemistry. In this present research, we set up a novel chlorine dioxide-iodine-malonic acid chemical reaction model incorporating delays. The peculiarity of solution and Hopf bifurcation of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model are explored. Firstly, the existence and uniqueness is investigated via fixed point theorem. Secondly, the non-negativeness of solution is studied via some proper mathematical inequality shills. Thirdly, the stability and bifurcation of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model are analyzed. The influence of delay on the delayed chlorine dioxide-iodine-malonic acid chemical reaction model is uncovered. Fourthly, Hopf bifurcation control issue of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model is studied via two hybrid controllers. To check the soundness of acquired key assertions, Matlab simulations are executed. The gained assertions of this research are completely novel and possess tremendous theoretical value in maintaining the balance of the concentrations of chlorine dioxide, iodine in chemistry.
{"title":"Further Insight into Bifurcation and Hybrid Control Tactics of a Chlorine Dioxide-Iodine-Malonic Acid Chemical Reaction Model Incorporating Delays","authors":"D. Mu, Changjin Xu, Zixin Liu, Yicheng Pang","doi":"10.46793/match.89-3.529m","DOIUrl":"https://doi.org/10.46793/match.89-3.529m","url":null,"abstract":"Delayed differential equation is an important tool to describe the interaction of different chemical substance in chemistry. In this present research, we set up a novel chlorine dioxide-iodine-malonic acid chemical reaction model incorporating delays. The peculiarity of solution and Hopf bifurcation of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model are explored. Firstly, the existence and uniqueness is investigated via fixed point theorem. Secondly, the non-negativeness of solution is studied via some proper mathematical inequality shills. Thirdly, the stability and bifurcation of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model are analyzed. The influence of delay on the delayed chlorine dioxide-iodine-malonic acid chemical reaction model is uncovered. Fourthly, Hopf bifurcation control issue of the formulated delayed chlorine dioxide-iodine-malonic acid chemical reaction model is studied via two hybrid controllers. To check the soundness of acquired key assertions, Matlab simulations are executed. The gained assertions of this research are completely novel and possess tremendous theoretical value in maintaining the balance of the concentrations of chlorine dioxide, iodine in chemistry.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82287347","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 : 2023-01-01DOI: 10.46793/match.89-3.733o
M. Oboudi
{"title":"The Mean Value of Sombor Index of Graphs","authors":"M. Oboudi","doi":"10.46793/match.89-3.733o","DOIUrl":"https://doi.org/10.46793/match.89-3.733o","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90472785","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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