{"title":"生成三连平面线图","authors":"Phoebe Hollowbread-Smith , Riccardo W. Maffucci","doi":"10.1016/j.disc.2024.114302","DOIUrl":null,"url":null,"abstract":"<div><div>We classify and construct all line graphs that are 3-polytopes (planar and 3-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., 3-regular) 3-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of 3-polytopes <span><span>[6]</span></span>, <span><span>[13]</span></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 2","pages":"Article 114302"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generation of 3-connected, planar line graphs\",\"authors\":\"Phoebe Hollowbread-Smith , Riccardo W. Maffucci\",\"doi\":\"10.1016/j.disc.2024.114302\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We classify and construct all line graphs that are 3-polytopes (planar and 3-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., 3-regular) 3-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of 3-polytopes <span><span>[6]</span></span>, <span><span>[13]</span></span>.</div></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":\"348 2\",\"pages\":\"Article 114302\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24004333\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24004333","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We classify and construct all line graphs that are 3-polytopes (planar and 3-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., 3-regular) 3-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of 3-polytopes [6], [13].
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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