N-dimensional maps are combinatorial models defined for representing the topology of subdivisions of n-dimensional geometric spaces, i.e., the topology of partitions of the spaces into i-dimensional cells (vertices, edges, faces, volumes, etc.; 0≤i≤n) [P. Lienhardt, Internat. J. Comput. Geom. Appl. 4 (1994), no. 3, 275–324; MR1296150 (95h:52029)]. They provide the basis for a simple, uniform, and general computer representation of the relative spatial arrangement of atoms in stereogenic entities. This article illustrates the use of 2-dimensional maps as a non-geometric computer representation of convex polyhedral and polygonal stereogenic entities, thus covering the vast majority of stereochemical atomic configurations, bond conformations, etc.
{"title":"Representation of stereochemistry using combinatorial maps","authors":"A. Dietz, C. Fiorio, M. Habib, C. Laurenço","doi":"10.1090/dimacs/051/09","DOIUrl":"https://doi.org/10.1090/dimacs/051/09","url":null,"abstract":"N-dimensional maps are combinatorial models defined for representing the topology of subdivisions of n-dimensional geometric spaces, i.e., the topology of partitions of the spaces into i-dimensional cells (vertices, edges, faces, volumes, etc.; 0≤i≤n) [P. Lienhardt, Internat. J. Comput. Geom. Appl. 4 (1994), no. 3, 275–324; MR1296150 (95h:52029)]. They provide the basis for a simple, uniform, and general computer representation of the relative spatial arrangement of atoms in stereogenic entities. This article illustrates the use of 2-dimensional maps as a non-geometric computer representation of convex polyhedral and polygonal stereogenic entities, thus covering the vast majority of stereochemical atomic configurations, bond conformations, etc.","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1998-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124230377","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":"Star sets and star complements in finite graphs: A spectral construction technique","authors":"P. Rowlinson","doi":"10.1090/dimacs/051/24","DOIUrl":"https://doi.org/10.1090/dimacs/051/24","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116080858","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":"Enumeration of fusenes to h = 20","authors":"G. Caporossi, P. Hansen, M. Zheng","doi":"10.1090/dimacs/051/05","DOIUrl":"https://doi.org/10.1090/dimacs/051/05","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122858031","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":"An efficient algorithm for determining fixed bonds and normal components in a bipartite graph","authors":"Xiaofeng Guo, M. Randic","doi":"10.1090/dimacs/051/13","DOIUrl":"https://doi.org/10.1090/dimacs/051/13","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128128234","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":"Characterizing properties of some graph invariants related to electron charges in the Hückel molecular orbital theory","authors":"D. Cvetkovic","doi":"10.1090/dimacs/051/06","DOIUrl":"https://doi.org/10.1090/dimacs/051/06","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131351805","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":"Numerical solutions of the Laplace equation in chemical spaces","authors":"R. Hefferlin","doi":"10.1090/dimacs/051/14","DOIUrl":"https://doi.org/10.1090/dimacs/051/14","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129969670","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":"Geometrical and combinatorial questions about fullerenes","authors":"J. Malkevitch","doi":"10.1090/dimacs/051/19","DOIUrl":"https://doi.org/10.1090/dimacs/051/19","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127074003","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 so called ring spiral algorithm is a convenient means for gen erating and representing certain fullerenes and some other cubic poly hedra In Manolopoulos and Fowler presented a fullerene on vertices without a spiral No smaller unspirable fullerene is known In the spring of using computer Gunnar Brinkmann found the smallest cubic polyhedron without a spiral It has only vertices Here we generalize the ring spiral approach in order to obtain a canon ical representation for arbitrary planar cubic polyhedra Some other questions are addressed for instance possible generalization of this method to polyhedra of higher genus and to polyhedra with vertices of arbitrary valency
{"title":"A generalized ring spiral algorithm for coding fullerenes and other cubic polyhedra","authors":"P. Fowler, T. Pisanski, A. Graovac, J. Žerovnik","doi":"10.1090/dimacs/051/12","DOIUrl":"https://doi.org/10.1090/dimacs/051/12","url":null,"abstract":"The so called ring spiral algorithm is a convenient means for gen erating and representing certain fullerenes and some other cubic poly hedra In Manolopoulos and Fowler presented a fullerene on vertices without a spiral No smaller unspirable fullerene is known In the spring of using computer Gunnar Brinkmann found the smallest cubic polyhedron without a spiral It has only vertices Here we generalize the ring spiral approach in order to obtain a canon ical representation for arbitrary planar cubic polyhedra Some other questions are addressed for instance possible generalization of this method to polyhedra of higher genus and to polyhedra with vertices of arbitrary valency","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122770872","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":"Use of graph invariants in QMSA and predictive toxicology","authors":"S. Basak, B. Gute","doi":"10.1090/dimacs/051/02","DOIUrl":"https://doi.org/10.1090/dimacs/051/02","url":null,"abstract":"","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115673697","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 aim is a description of discrete mathematics used in a project 1 devoted to the implementation of a software package for the simulation of combinatorial chemistry. A. Hage-dorn contributes to this crossing the interface" by making helpful remarks on applications of quantum mechanical resonances, which play an important role in chemical reactions. The report of the National Academy is very useful, since it brings a very important eld of applications of all kinds of mathematics into focus, listing
{"title":"Discrete mathematics for combinatorial chemistry","authors":"A. Kerber, R. Laue, T. Wieland","doi":"10.1090/dimacs/051/16","DOIUrl":"https://doi.org/10.1090/dimacs/051/16","url":null,"abstract":"The aim is a description of discrete mathematics used in a project 1 devoted to the implementation of a software package for the simulation of combinatorial chemistry. A. Hage-dorn contributes to this crossing the interface\" by making helpful remarks on applications of quantum mechanical resonances, which play an important role in chemical reactions. The report of the National Academy is very useful, since it brings a very important eld of applications of all kinds of mathematics into focus, listing","PeriodicalId":145977,"journal":{"name":"Discrete Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116419205","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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