双图和迈锡尔图中的互见性和一般位置

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2024-10-17 DOI:10.1016/j.amc.2024.129131

Dhanya Roy , Sandi Klavžar , Aparna Lakshmanan S

{"title":"双图和迈锡尔图中的互见性和一般位置","authors":"Dhanya Roy , Sandi Klavžar , Aparna Lakshmanan S","doi":"10.1016/j.amc.2024.129131","DOIUrl":null,"url":null,"abstract":"<div><div>The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"488 ","pages":"Article 129131"},"PeriodicalIF":3.5000,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mutual-visibility and general position in double graphs and in Mycielskians\",\"authors\":\"Dhanya Roy , Sandi Klavžar , Aparna Lakshmanan S\",\"doi\":\"10.1016/j.amc.2024.129131\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles.</div></div>\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":\"488 \",\"pages\":\"Article 129131\"},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324005927\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324005927","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

图中的一般位置问题是找到最大可能的顶点集合，其性质是其中没有三个顶点位于共同的最短路径上。图中的互见性问题是找到可以选择的最大顶点数，使得集合中的每对顶点之间都有一条最短路径，且集合中没有顶点作为内部顶点。这里研究的是双图和迈锡尔图中的一般位置问题和互见性问题。证明了尖锐的一般界限，特别是涉及基图的总互见数和外互见数。此外，还确定了几个精确值，特别是双图和循环 Mycielskian 的互见数。

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

Mutual-visibility and general position in double graphs and in Mycielskians

The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles.

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

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.