{"title":"On hypercycles and hypercircuits in hypergraphs","authors":"A. V. Zeigarnik","doi":"10.1090/dimacs/051/28","DOIUrl":"https://doi.org/10.1090/dimacs/051/28","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122043550","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}
The design of a synthesis strategy in Organic Chemistry rests on the perception of the target molecule. This one has to be perceived from several viewpoints: topology, stereochemistry, functionality... We propose an abstract representation of molecules which describes the topological viewpoint (cycles, carbon chains and their structural relationships). This representation is based on a polynomial algorithm that computes the set of relevant cycles in the molecular graph. This set is equal to the union of all the minimum cycle bases of the graph. The abstract representation is integrated in RESYN, a system for computer-aided organic synthesis planning.
{"title":"An abstract representation for molecular graphs","authors":"P. Vismara, C. Laurenço","doi":"10.1090/dimacs/051/26","DOIUrl":"https://doi.org/10.1090/dimacs/051/26","url":null,"abstract":"The design of a synthesis strategy in Organic Chemistry rests on the perception of the target molecule. This one has to be perceived from several viewpoints: topology, stereochemistry, functionality... We propose an abstract representation of molecules which describes the topological viewpoint (cycles, carbon chains and their structural relationships). This representation is based on a polynomial algorithm that computes the set of relevant cycles in the molecular graph. This set is equal to the union of all the minimum cycle bases of the graph. The abstract representation is integrated in RESYN, a system for computer-aided organic synthesis planning.","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125025545","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}
Abstract. Applications of isometric embeddings of benzenoid graphs are surveyed. Their embeddings into hypercubes provide methods for computing the Wiener index and the Szeged index, while embeddings into the Cartesian product of trees lead to fast algorithms. A new method for computing the hyperWiener index of partial cubes in general, and of benzenoid graphs and trees in particular, is also presented.
{"title":"Applications of isometric embeddings to chemical graphs","authors":"S. Klavžar","doi":"10.1090/dimacs/051/18","DOIUrl":"https://doi.org/10.1090/dimacs/051/18","url":null,"abstract":"Abstract. Applications of isometric embeddings of benzenoid graphs are surveyed. Their embeddings into hypercubes provide methods for computing the Wiener index and the Szeged index, while embeddings into the Cartesian product of trees lead to fast algorithms. A new method for computing the hyperWiener index of partial cubes in general, and of benzenoid graphs and trees in particular, is also presented.","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130630079","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}
{"title":"Random networks in two dimensions. Simulations and correlations","authors":"H. Ohlenbusch, N. Rivier, T. Aste, B. Dubertret","doi":"10.1090/dimacs/051/21","DOIUrl":"https://doi.org/10.1090/dimacs/051/21","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":"254 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133232002","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}
{"title":"Foldedness in linear polymers: A difference between graphical and Euclidean distances","authors":"L. Bytautas, D. Klein, M. Randic, T. Pisanski","doi":"10.1090/dimacs/051/04","DOIUrl":"https://doi.org/10.1090/dimacs/051/04","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125180317","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}
{"title":"(3-6)-cages, Hexagonal Toroidal Cages, and Their Spectra","authors":"P. Fowler, P. John, H. Sachs","doi":"10.1090/dimacs/051/11","DOIUrl":"https://doi.org/10.1090/dimacs/051/11","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117105783","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}
{"title":"Group and graph theoretical perspectives on the structures of large icosahedral cages","authors":"C. M. Quinn, D. B. Redmond, P. Fowler","doi":"10.1090/dimacs/051/22","DOIUrl":"https://doi.org/10.1090/dimacs/051/22","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":"176 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116397721","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}
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