Pub Date : 2023-01-01DOI: 10.46793/match.89-3.643y
Luzhen Ye
{"title":"New Variants of Gutman’s Formulas on the Algebraic Structure Count","authors":"Luzhen Ye","doi":"10.46793/match.89-3.643y","DOIUrl":"https://doi.org/10.46793/match.89-3.643y","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"133 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73765950","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 : 2022-12-29DOI: 10.46793/match.90-1.187t
Hanjo Taubig
In a recent article, Nadeem and Siddique used Chebyshev’s sum inequality to establish the Zagreb indices inequality M1/n ≤ M2/m for undirected graphs in the case where the degree sequence (di) and the degree-sum sequence (Si) are similarly ordered. We show that this is actually not a completely new result and we discuss several related results that also cover similar inequalities for directed graphs, as well as sum-symmetric matrices and Eulerian directed graphs.
{"title":"Chebyshev's Sum Inequality and the Zagreb Indices Inequality","authors":"Hanjo Taubig","doi":"10.46793/match.90-1.187t","DOIUrl":"https://doi.org/10.46793/match.90-1.187t","url":null,"abstract":"In a recent article, Nadeem and Siddique used Chebyshev’s sum inequality to establish the Zagreb indices inequality M1/n ≤ M2/m for undirected graphs in the case where the degree sequence (di) and the degree-sum sequence (Si) are similarly ordered. We show that this is actually not a completely new result and we discuss several related results that also cover similar inequalities for directed graphs, as well as sum-symmetric matrices and Eulerian directed graphs.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"6 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87582179","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 : 2022-11-22DOI: 10.46793/match.90-1.197d
Ivan Damnjanovi'c, Marko Milovsevi'c, Dragan Stevanovi'c
We note here that the problem of determining extremal values of Sombor index for trees with a given degree sequence fits within the framework of results by Hua Wang from [Cent. Eur. J. Math. 12 (2014) 1656-1663], implying that the greedy tree has the minimum Sombor index, while an alternating greedy tree has the maximum Sombor index.
{"title":"A Note on Extremal Sombor Indices of Trees with a Given Degree Sequence","authors":"Ivan Damnjanovi'c, Marko Milovsevi'c, Dragan Stevanovi'c","doi":"10.46793/match.90-1.197d","DOIUrl":"https://doi.org/10.46793/match.90-1.197d","url":null,"abstract":"We note here that the problem of determining extremal values of Sombor index for trees with a given degree sequence fits within the framework of results by Hua Wang from [Cent. Eur. J. Math. 12 (2014) 1656-1663], implying that the greedy tree has the minimum Sombor index, while an alternating greedy tree has the maximum Sombor index.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"13 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74987322","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.89-1.005s
Georgii N. Sizov, E. Babaev
In the article, at the mathematical level of rigor, it is shown that the pair of concepts "covalence – mesoionicity" correlates in the same way as the pair "kekuleness – non-kekuleness". A criterion for a structure to be mesoionic (mesoionicity criterion) is formulated and proved, which makes it possible to enumerate all mono-charged mesoionic structures (mesomeric betaines) on a given graph. The mesoionicity criterion and the Kasteleyn theorem (on counting the number of perfect matchings in a graph) were used as the basis for a computer program that classifies dipolar resonance structures. The work of the program is demonstrated on the lists of obtained mesoionic structures. A general approach to mesoionicity is discussed.
{"title":"Criteria for a Structure to be Mesoionic","authors":"Georgii N. Sizov, E. Babaev","doi":"10.46793/match.89-1.005s","DOIUrl":"https://doi.org/10.46793/match.89-1.005s","url":null,"abstract":"In the article, at the mathematical level of rigor, it is shown that the pair of concepts \"covalence – mesoionicity\" correlates in the same way as the pair \"kekuleness – non-kekuleness\". A criterion for a structure to be mesoionic (mesoionicity criterion) is formulated and proved, which makes it possible to enumerate all mono-charged mesoionic structures (mesomeric betaines) on a given graph. The mesoionicity criterion and the Kasteleyn theorem (on counting the number of perfect matchings in a graph) were used as the basis for a computer program that classifies dipolar resonance structures. The work of the program is demonstrated on the lists of obtained mesoionic structures. A general approach to mesoionicity is discussed.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"24 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80136566","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.89-2.451r
Mohammed Selim Reja, S. M. Abu Nayeem
{"title":"On Sombor Index and Graph Energy","authors":"Mohammed Selim Reja, S. M. Abu Nayeem","doi":"10.46793/match.89-2.451r","DOIUrl":"https://doi.org/10.46793/match.89-2.451r","url":null,"abstract":"","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":"91234081","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.89-1.175s
Gergely Szlobodnyik, G. Szederkényi
In this paper the reachability problem of discrete state Chemical Reaction Networks (d-CRNs) is studied. We consider sub-classes of sub-and superconservative d-CRN network structures and prove that the reachability relation can be decided in polynomial time. We make use of the result that in the studied d-CRN sub-classes, the reachability relation is equivalent to the existence of a non-negative integer solution of the d-CRN state equation. The equivalence implies the reformulation of the reachability problem as integer linear programming decision problem. We show that in the studied classes of d-CRN structures, the state equation has a totally unimodular coefficient matrix. As the reachability relation is equivalent to the non-negative integer solution of the state equation, the resulting integer programming decision program can be relaxed to a simple linear program having polynomial time complexity. Hence, in the studied sub-classes of sub and superconservative reaction network structures, the reachability relation can be decided in polynomial time and the number of continuous decision variables is equal to the number of reactions of the d-CRN.
{"title":"Polynomial Time Reachability Analysis in Discrete State Chemical Reaction Networks Obeying Conservation Laws","authors":"Gergely Szlobodnyik, G. Szederkényi","doi":"10.46793/match.89-1.175s","DOIUrl":"https://doi.org/10.46793/match.89-1.175s","url":null,"abstract":"In this paper the reachability problem of discrete state Chemical Reaction Networks (d-CRNs) is studied. We consider sub-classes of sub-and superconservative d-CRN network structures and prove that the reachability relation can be decided in polynomial time. We make use of the result that in the studied d-CRN sub-classes, the reachability relation is equivalent to the existence of a non-negative integer solution of the d-CRN state equation. The equivalence implies the reformulation of the reachability problem as integer linear programming decision problem. We show that in the studied classes of d-CRN structures, the state equation has a totally unimodular coefficient matrix. As the reachability relation is equivalent to the non-negative integer solution of the state equation, the resulting integer programming decision program can be relaxed to a simple linear program having polynomial time complexity. Hence, in the studied sub-classes of sub and superconservative reaction network structures, the reachability relation can be decided in polynomial time and the number of continuous decision variables is equal to the number of reactions of the d-CRN.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"37 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75100449","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.89-1.049a
M. S. Akram, M. Usman, F. S. AlHumaidan
The Horiuti-Polanyi (HP) mechanism has been studied for the methylcyclohexane dehydrogenation reaction over a Pt/AlO catalyst. Three HP mechanistic schemes such as competitive, non-competitive, and combined-competitive-non-competitive were used in the kinetic modeling of the experimental data. The loss of first hydrogen atom was regarded as the rate-determining step and the mathematical expressions were developed and fitted against the data. A FORTRAN routine was employed where 4th order Runge-Kutta method was used to solve the related differential equation and Marquardt algorithm was used for the parametric estimation. A kinetically and statistically best-fit HP kinetic equation was obtained with 87.96 kJ/mol of activation energy. The best-fit kinetic model was tested with five additional Pt-containing AlO catalysts and yet again found in good agreement with the experimental data.
{"title":"Mathematical and Kinetic Study of Horiuti-Polanyi Reaction Mechanism for the Methylcyclohexane Dehydrogenation Over Various Pt/Al2O3 Catalysts","authors":"M. S. Akram, M. Usman, F. S. AlHumaidan","doi":"10.46793/match.89-1.049a","DOIUrl":"https://doi.org/10.46793/match.89-1.049a","url":null,"abstract":"The Horiuti-Polanyi (HP) mechanism has been studied for the methylcyclohexane dehydrogenation reaction over a Pt/AlO catalyst. Three HP mechanistic schemes such as competitive, non-competitive, and combined-competitive-non-competitive were used in the kinetic modeling of the experimental data. The loss of first hydrogen atom was regarded as the rate-determining step and the mathematical expressions were developed and fitted against the data. A FORTRAN routine was employed where 4th order Runge-Kutta method was used to solve the related differential equation and Marquardt algorithm was used for the parametric estimation. A kinetically and statistically best-fit HP kinetic equation was obtained with 87.96 kJ/mol of activation energy. The best-fit kinetic model was tested with five additional Pt-containing AlO catalysts and yet again found in good agreement with the experimental data.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85414820","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.89-2.489o
M. Oboudi, M. Nematollahi
{"title":"Improving a Lower Bound for Seidel Energy of Graphs","authors":"M. Oboudi, M. Nematollahi","doi":"10.46793/match.89-2.489o","DOIUrl":"https://doi.org/10.46793/match.89-2.489o","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"44 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81583283","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.89-1.223o
M. Oz
The Hosoya index of is defined as the total number of independent edge sets (number of -matchings ) in . The Hosoya index is one of the most important topological indices in the field of mathematical chemistry because of its relationship with several thermodynamic properties. Therefore, computation of the number of -matchings of various molecular structures has importance. Two methods, one for computing the number of the Hosoya index of catacondensed benzenoid systems and the other for the number of -matchings in benzenoid chains (unbranched catacondensed benzenoid systems), have been presented so far. In this paper, a method based on some transfer matrices to compute the number of -matchings of arbitrary (both unbranched and branched) catacondensed benzenoid systems is presented. Moreover, some algorithms are designed to keep the applicability of the method the same as increases.
{"title":"Computing the Number of Matchings in Catacondensed Benzenoid Systems","authors":"M. Oz","doi":"10.46793/match.89-1.223o","DOIUrl":"https://doi.org/10.46793/match.89-1.223o","url":null,"abstract":"The Hosoya index of is defined as the total number of independent edge sets (number of -matchings ) in . The Hosoya index is one of the most important topological indices in the field of mathematical chemistry because of its relationship with several thermodynamic properties. Therefore, computation of the number of -matchings of various molecular structures has importance. Two methods, one for computing the number of the Hosoya index of catacondensed benzenoid systems and the other for the number of -matchings in benzenoid chains (unbranched catacondensed benzenoid systems), have been presented so far. In this paper, a method based on some transfer matrices to compute the number of -matchings of arbitrary (both unbranched and branched) catacondensed benzenoid systems is presented. Moreover, some algorithms are designed to keep the applicability of the method the same as increases.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"30 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73249695","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.89-2.301n
R. M. Nemba, Thomas B. Makon, Aline Nodem
{"title":"Linear Spaces of Permutomers and Symmetry Itemized Isomers Numbers of C2v-based Cuneane Derivatives and Heteroanalogues. II","authors":"R. M. Nemba, Thomas B. Makon, Aline Nodem","doi":"10.46793/match.89-2.301n","DOIUrl":"https://doi.org/10.46793/match.89-2.301n","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"25 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77227441","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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