{"title":"星图与路径图笛卡尔积中标识码的界","authors":"J. P. Felix, Márcia R. Cappelle","doi":"10.5753/etc.2023.230607","DOIUrl":null,"url":null,"abstract":"In a graph, an identifying code (or ID code, for short) is a dominating set with the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. Thus every vertex can be uniquely identified by this intersection. The ID code number of a graph G is the minimum cardinality of an ID code of G and is denoted by γID(G). We present lower and upper bounds for γID in the Cartesian product of star and path graphs.","PeriodicalId":165974,"journal":{"name":"Anais do VIII Encontro de Teoria da Computação (ETC 2023)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bounds on Identifying Codes in the Cartesian Product of a Star and a Path Graph\",\"authors\":\"J. P. Felix, Márcia R. Cappelle\",\"doi\":\"10.5753/etc.2023.230607\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a graph, an identifying code (or ID code, for short) is a dominating set with the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. Thus every vertex can be uniquely identified by this intersection. The ID code number of a graph G is the minimum cardinality of an ID code of G and is denoted by γID(G). We present lower and upper bounds for γID in the Cartesian product of star and path graphs.\",\"PeriodicalId\":165974,\"journal\":{\"name\":\"Anais do VIII Encontro de Teoria da Computação (ETC 2023)\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Anais do VIII Encontro de Teoria da Computação (ETC 2023)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5753/etc.2023.230607\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Anais do VIII Encontro de Teoria da Computação (ETC 2023)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5753/etc.2023.230607","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bounds on Identifying Codes in the Cartesian Product of a Star and a Path Graph
In a graph, an identifying code (or ID code, for short) is a dominating set with the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. Thus every vertex can be uniquely identified by this intersection. The ID code number of a graph G is the minimum cardinality of an ID code of G and is denoted by γID(G). We present lower and upper bounds for γID in the Cartesian product of star and path graphs.
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