{"title":"大簇数图形的适当(强)彩虹连接和适当(强)彩虹顶点连接","authors":"Yingbin Ma, Yanfeng Xue, Xiaoxue Zhang","doi":"10.1142/s0219265923500342","DOIUrl":null,"url":null,"abstract":"The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] rainbow vertex connected. The proper strong rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] strong rainbow vertex connected. These two concepts are inspired by the concepts of proper (strong) rainbow connection number of graphs. In this paper, we determine the values of [Formula: see text] and [Formula: see text] of [Formula: see text] with large clique numbers [Formula: see text] and [Formula: see text]. Moreover, we determine the values of [Formula: see text] and [Formula: see text] of [Formula: see text] with large clique numbers [Formula: see text], [Formula: see text] and [Formula: see text].","PeriodicalId":53990,"journal":{"name":"JOURNAL OF INTERCONNECTION NETWORKS","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Proper (Strong) Rainbow Connection and Proper (Strong) Rainbow Vertex Connection of Graphs with Large Clique Number\",\"authors\":\"Yingbin Ma, Yanfeng Xue, Xiaoxue Zhang\",\"doi\":\"10.1142/s0219265923500342\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] rainbow vertex connected. The proper strong rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] strong rainbow vertex connected. These two concepts are inspired by the concepts of proper (strong) rainbow connection number of graphs. In this paper, we determine the values of [Formula: see text] and [Formula: see text] of [Formula: see text] with large clique numbers [Formula: see text] and [Formula: see text]. Moreover, we determine the values of [Formula: see text] and [Formula: see text] of [Formula: see text] with large clique numbers [Formula: see text], [Formula: see text] and [Formula: see text].\",\"PeriodicalId\":53990,\"journal\":{\"name\":\"JOURNAL OF INTERCONNECTION NETWORKS\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JOURNAL OF INTERCONNECTION NETWORKS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219265923500342\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF INTERCONNECTION NETWORKS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219265923500342","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Proper (Strong) Rainbow Connection and Proper (Strong) Rainbow Vertex Connection of Graphs with Large Clique Number
The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] rainbow vertex connected. The proper strong rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] to make [Formula: see text] strong rainbow vertex connected. These two concepts are inspired by the concepts of proper (strong) rainbow connection number of graphs. In this paper, we determine the values of [Formula: see text] and [Formula: see text] of [Formula: see text] with large clique numbers [Formula: see text] and [Formula: see text]. Moreover, we determine the values of [Formula: see text] and [Formula: see text] of [Formula: see text] with large clique numbers [Formula: see text], [Formula: see text] and [Formula: see text].
期刊介绍:
The Journal of Interconnection Networks (JOIN) is an international scientific journal dedicated to advancing the state-of-the-art of interconnection networks. The journal addresses all aspects of interconnection networks including their theory, analysis, design, implementation and application, and corresponding issues of communication, computing and function arising from (or applied to) a variety of multifaceted networks. Interconnection problems occur at different levels in the hardware and software design of communicating entities in integrated circuits, multiprocessors, multicomputers, and communication networks as diverse as telephone systems, cable network systems, computer networks, mobile communication networks, satellite network systems, the Internet and biological systems.