{"title":"保持w2属性的图运算","authors":"Vadim E. Levit, Eugen Mandrescu","doi":"10.1016/j.endm.2018.06.007","DOIUrl":null,"url":null,"abstract":"<div><p>A graph is <em>well-covered</em> if all its maximal independent sets are of the same size (Plummer, 1970). A graph <em>G</em> belongs to class <strong>W</strong><sub><em>n</em></sub> if every <em>n</em> pairwise disjoint independent sets in <em>G</em> are included in <em>n</em> pairwise disjoint maximum independent sets (Staples, 1975). Clearly, <strong>W</strong><sub>1</sub> is the family of all well-covered graphs. Staples showed a number of ways to build graphs in <strong>W</strong><sub><em>n</em></sub>, using graphs from <strong>W</strong><sub><em>n</em></sub> or <strong>W</strong><sub><em>n</em>+1</sub>. In this paper, we construct some more infinite subfamilies of the class <strong>W</strong><sub><strong>2</strong></sub> by means of corona, join, and rooted product of graphs.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.007","citationCount":"0","resultStr":"{\"title\":\"Graph Operations Preserving W2-Property\",\"authors\":\"Vadim E. Levit, Eugen Mandrescu\",\"doi\":\"10.1016/j.endm.2018.06.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A graph is <em>well-covered</em> if all its maximal independent sets are of the same size (Plummer, 1970). A graph <em>G</em> belongs to class <strong>W</strong><sub><em>n</em></sub> if every <em>n</em> pairwise disjoint independent sets in <em>G</em> are included in <em>n</em> pairwise disjoint maximum independent sets (Staples, 1975). Clearly, <strong>W</strong><sub>1</sub> is the family of all well-covered graphs. Staples showed a number of ways to build graphs in <strong>W</strong><sub><em>n</em></sub>, using graphs from <strong>W</strong><sub><em>n</em></sub> or <strong>W</strong><sub><em>n</em>+1</sub>. In this paper, we construct some more infinite subfamilies of the class <strong>W</strong><sub><strong>2</strong></sub> by means of corona, join, and rooted product of graphs.</p></div>\",\"PeriodicalId\":35408,\"journal\":{\"name\":\"Electronic Notes in Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.007\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Notes in Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1571065318300982\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571065318300982","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A graph G belongs to class Wn if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W1 is the family of all well-covered graphs. Staples showed a number of ways to build graphs in Wn, using graphs from Wn or Wn+1. In this paper, we construct some more infinite subfamilies of the class W2 by means of corona, join, and rooted product of graphs.
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Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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