Pub Date : 2022-08-01DOI: 10.46793/match.89-1.245i
G. De Ita, Pedro Bello, Meliza Contreras
We present a method for computing the Merrifield-Simmons index on some basic graphs. For example, our proposal works on paths, simple cycles, trees, and we show that the method can be extended to process benzenoid systems Hr,t with a total of r.t hexagons. In the case of benzenoid systems, our method consists of performing a linear-time Hamiltonian walking on an isomorphic hexagonal grid from , at the same time that the number of independent sets are being computed incrementally. Our method improves the asymptotic behavior of the time-complexity with respect to the transfer matrix method, which is the classic method for computing the Merrifield-Simmons index on grid graphs, even for benzenoid systems.
{"title":"A Method for Computing the Merrifield–Simmons Index on Benzenoid Systems","authors":"G. De Ita, Pedro Bello, Meliza Contreras","doi":"10.46793/match.89-1.245i","DOIUrl":"https://doi.org/10.46793/match.89-1.245i","url":null,"abstract":"We present a method for computing the Merrifield-Simmons index on some basic graphs. For example, our proposal works on paths, simple cycles, trees, and we show that the method can be extended to process benzenoid systems Hr,t with a total of r.t hexagons. In the case of benzenoid systems, our method consists of performing a linear-time Hamiltonian walking on an isomorphic hexagonal grid from , at the same time that the number of independent sets are being computed incrementally. Our method improves the asymptotic behavior of the time-complexity with respect to the transfer matrix method, which is the classic method for computing the Merrifield-Simmons index on grid graphs, even for benzenoid systems.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"74 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77413762","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.89-1.073x
Changjin Xu, D. Mu, Zixin Liu, Yicheng Pang, C. Aouiti, O. Tunç, Shabir Ahmad, A. Zeb
Building differential dynamical systems to describe the changing relationship among chemical components is a vital aspect in chemistry. In this present manuscript, we put forward a new fractional-order delayed Brusselator chemical reaction model. By virtue of contraction mapping principle, we investigate the existence and uniqueness of the solution of fractional-order delayed Brusselator chemical reaction model. With the aid of mathematical analysis technique, we consider the non-negativeness of the solution of the fractional-order delayed Brusselator chemical reaction model. Making use of the theory of fractional-order dynamical system, we explore the stability and Hopf bifurcation issue of the fractional-order delayed Brusselator chemical reaction model. By designing a reasonable controller, we have availably controlled the time of emergence of Hopf bifurcation of the fractional-order delayed Brusselator chemical reaction model. A sufficient criterion guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled delayed Brusselator chemical reaction model is set up. Computer simulations are implemented to validate the theoretical findings. The derived fruits of this manuscript have great theoretical significance in controlling the concentrations of chemical substances.
{"title":"Bifurcation Dynamics and Control Mechanism of a Fractional-Order Delayed Brusselator Chemical Reaction Model","authors":"Changjin Xu, D. Mu, Zixin Liu, Yicheng Pang, C. Aouiti, O. Tunç, Shabir Ahmad, A. Zeb","doi":"10.46793/match.89-1.073x","DOIUrl":"https://doi.org/10.46793/match.89-1.073x","url":null,"abstract":"Building differential dynamical systems to describe the changing relationship among chemical components is a vital aspect in chemistry. In this present manuscript, we put forward a new fractional-order delayed Brusselator chemical reaction model. By virtue of contraction mapping principle, we investigate the existence and uniqueness of the solution of fractional-order delayed Brusselator chemical reaction model. With the aid of mathematical analysis technique, we consider the non-negativeness of the solution of the fractional-order delayed Brusselator chemical reaction model. Making use of the theory of fractional-order dynamical system, we explore the stability and Hopf bifurcation issue of the fractional-order delayed Brusselator chemical reaction model. By designing a reasonable controller, we have availably controlled the time of emergence of Hopf bifurcation of the fractional-order delayed Brusselator chemical reaction model. A sufficient criterion guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled delayed Brusselator chemical reaction model is set up. Computer simulations are implemented to validate the theoretical findings. The derived fruits of this manuscript have great theoretical significance in controlling the concentrations of chemical substances.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"186 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77759666","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.89-2.467r
B. Rather, Muhammad Imran
{"title":"A Note on Energy and Sombor Energy of Graphs","authors":"B. Rather, Muhammad Imran","doi":"10.46793/match.89-2.467r","DOIUrl":"https://doi.org/10.46793/match.89-2.467r","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"485 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75130257","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.89-2.371d
Shiikhar Dorjsembe, Lkhagva Buyantogtokh, I. Gutman, B. Horoldagva, T. Réti
{"title":"Irregularity of Graphs","authors":"Shiikhar Dorjsembe, Lkhagva Buyantogtokh, I. Gutman, B. Horoldagva, T. Réti","doi":"10.46793/match.89-2.371d","DOIUrl":"https://doi.org/10.46793/match.89-2.371d","url":null,"abstract":"","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":"85062041","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 : 2022-07-07DOI: 10.46793/match.89-2.343s
Rui Song, Qiongxiang Huang
: A topological index reflects the physical, chemical and structural properties of a molecule, and its study has an important role in molecular topology, chemical graph theory and mathematical chemistry. It is a natural problem to characterize non-isomorphic graphs with the same topological index value. By introducing a relation on trees with respect to edge division vectors, denoted by hT n , (cid:22)i , in this paper we give some results for the relation order in hT n , (cid:22)i , it allows us to compare the size of the topological index value without relying on the specific forms of them, and naturally we can determine which trees have the same topological index value. Based on these results we characterize some classes of trees that are uniquely determined by their edge division vectors and construct infinite classes of non-isomorphic trees with the same topological index value, particularly such trees of order no more than 10 are completely determined.
{"title":"A Relation on Trees and the Topological Indices Based on Subgraph","authors":"Rui Song, Qiongxiang Huang","doi":"10.46793/match.89-2.343s","DOIUrl":"https://doi.org/10.46793/match.89-2.343s","url":null,"abstract":": A topological index reflects the physical, chemical and structural properties of a molecule, and its study has an important role in molecular topology, chemical graph theory and mathematical chemistry. It is a natural problem to characterize non-isomorphic graphs with the same topological index value. By introducing a relation on trees with respect to edge division vectors, denoted by hT n , (cid:22)i , in this paper we give some results for the relation order in hT n , (cid:22)i , it allows us to compare the size of the topological index value without relying on the specific forms of them, and naturally we can determine which trees have the same topological index value. Based on these results we characterize some classes of trees that are uniquely determined by their edge division vectors and construct infinite classes of non-isomorphic trees with the same topological index value, particularly such trees of order no more than 10 are completely determined.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"38 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85722181","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 : 2022-05-06DOI: 10.46793/match.89-2.389c
Stijn Cambie, Matteo Mazzamurro
The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. In this paper, we characterize the connected graphs with given order n and size m that minimize the first degree-based entropy whenever n − 1 ≤ m ≤ 2 n − 3 , thus extending and proving a conjecture by Yan.
{"title":"Resolution of Yan's Conjecture on Entropy of Graphs","authors":"Stijn Cambie, Matteo Mazzamurro","doi":"10.46793/match.89-2.389c","DOIUrl":"https://doi.org/10.46793/match.89-2.389c","url":null,"abstract":"The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. In this paper, we characterize the connected graphs with given order n and size m that minimize the first degree-based entropy whenever n − 1 ≤ m ≤ 2 n − 3 , thus extending and proving a conjecture by Yan.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77113722","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 : 2022-04-01DOI: 10.46793/match.88-3.643r
Z. Raza, S. Balachandran, S. Elumalai, Akbar Ali
{"title":"On General Sum-Connectivity Index of Trees of Fixed Maximum Degree and Order","authors":"Z. Raza, S. Balachandran, S. Elumalai, Akbar Ali","doi":"10.46793/match.88-3.643r","DOIUrl":"https://doi.org/10.46793/match.88-3.643r","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72653871","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 : 2022-04-01DOI: 10.46793/match.88-3.535g
Wei Gao
{"title":"Trees with Maximum Vertex-Degree-Based Topological Indices","authors":"Wei Gao","doi":"10.46793/match.88-3.535g","DOIUrl":"https://doi.org/10.46793/match.88-3.535g","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"12 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84170767","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 : 2022-04-01DOI: 10.46793/match.88-3.573l
Hechao Liu, L. You, Yufei Huang
{"title":"Extremal Sombor Indices of Tetracyclic (Chemical) Graphs","authors":"Hechao Liu, L. You, Yufei Huang","doi":"10.46793/match.88-3.573l","DOIUrl":"https://doi.org/10.46793/match.88-3.573l","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"1 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89868428","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 : 2022-04-01DOI: 10.46793/match.88-3.481c
Roberto Cruz, J. Rada, Wilson Sanchez
n this paper we present a general criteria to decide when the cycle on vertices and , the coalescence of the star with the cycle , are extremal unicyclic graphs of a vertex-degree-based (VDB) topological index. We show that many of the well known results on extremal values of VDB topological indices over unicyclic graphs can be obtained as particular cases of ours. Moreover, we obtain new results on extremal values of VDB topological indices, such as the generalized Geometric-Arithmetic indices, the generalized Atom-Bond-Connectivity indices, and its exponentials, among others.
{"title":"Extremal Unicyclic Graphs with Respect to Vertex-Degree-Based Topological Indices","authors":"Roberto Cruz, J. Rada, Wilson Sanchez","doi":"10.46793/match.88-3.481c","DOIUrl":"https://doi.org/10.46793/match.88-3.481c","url":null,"abstract":"n this paper we present a general criteria to decide when the cycle on vertices and , the coalescence of the star with the cycle , are extremal unicyclic graphs of a vertex-degree-based (VDB) topological index. We show that many of the well known results on extremal values of VDB topological indices over unicyclic graphs can be obtained as particular cases of ours. Moreover, we obtain new results on extremal values of VDB topological indices, such as the generalized Geometric-Arithmetic indices, the generalized Atom-Bond-Connectivity indices, and its exponentials, among others.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"15 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75915497","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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