无爪三次图中的半全数强迫

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2023-01-01 DOI:10.7151/dmgt.2501

Yijuan Liang, Jie Chen, Shou-Jun Xu

{"title":"无爪三次图中的半全数强迫","authors":"Yijuan Liang, Jie Chen, Shou-Jun Xu","doi":"10.7151/dmgt.2501","DOIUrl":null,"url":null,"abstract":"For an isolate-free graph G = ( V ( G ) , E ( G )), a set S ⊆ V ( G ) is called a semitotal forcing set of G if it is a forcing set (or a zero forcing set) of G and every vertex in S is within distance 2 of another vertex of S . The semitotal forcing number F t 2 ( G ) is the minimum cardinality of a semitotal forcing set in G . In this paper, we prove that if G (cid:54) = K 4 is a connected claw-free cubic graph of order n , then F t 2 ( G ) ≤ 38 n + 1. The graphs achieving equality in this bound are characterized, an inﬁnite set of graphs.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":"1 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semitotal forcing in claw-free cubic graphs\",\"authors\":\"Yijuan Liang, Jie Chen, Shou-Jun Xu\",\"doi\":\"10.7151/dmgt.2501\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For an isolate-free graph G = ( V ( G ) , E ( G )), a set S ⊆ V ( G ) is called a semitotal forcing set of G if it is a forcing set (or a zero forcing set) of G and every vertex in S is within distance 2 of another vertex of S . The semitotal forcing number F t 2 ( G ) is the minimum cardinality of a semitotal forcing set in G . In this paper, we prove that if G (cid:54) = K 4 is a connected claw-free cubic graph of order n , then F t 2 ( G ) ≤ 38 n + 1. The graphs achieving equality in this bound are characterized, an inﬁnite set of graphs.\",\"PeriodicalId\":48875,\"journal\":{\"name\":\"Discussiones Mathematicae Graph Theory\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discussiones Mathematicae Graph Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7151/dmgt.2501\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discussiones Mathematicae Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7151/dmgt.2501","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于无隔离图G = (V (G)， E (G))，如果集合S是G的一个强迫集(或零强迫集)，且S中的每个顶点与S的另一个顶点的距离在2以内，则称其为G的半强迫集。半衰期强迫数f2 (G)是G中半衰期强迫集的最小基数。本文证明了如果G (cid:54) = k4是一个n阶的连通无爪三次图，则F t 2 (G)≤38n + 1。在这个界内达到相等的图被表示为图的无限集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Semitotal forcing in claw-free cubic graphs

For an isolate-free graph G = ( V ( G ) , E ( G )), a set S ⊆ V ( G ) is called a semitotal forcing set of G if it is a forcing set (or a zero forcing set) of G and every vertex in S is within distance 2 of another vertex of S . The semitotal forcing number F t 2 ( G ) is the minimum cardinality of a semitotal forcing set in G . In this paper, we prove that if G (cid:54) = K 4 is a connected claw-free cubic graph of order n , then F t 2 ( G ) ≤ 38 n + 1. The graphs achieving equality in this bound are characterized, an inﬁnite set of graphs.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.