{"title":"On the Extremal Values of the Weighted Integrity of a Graph","authors":"Wayne Goddard, Julia VanLandingham","doi":"10.1142/s0219265923500196","DOIUrl":null,"url":null,"abstract":"The integrity of a graph [Formula: see text] is defined as the minimum value of [Formula: see text] taken over all [Formula: see text], where [Formula: see text] denotes the maximum cardinality of a component of graph [Formula: see text]. In this paper, we investigate bounds on the maximum and minimum values of the weighted version of this parameter. We also consider the same question for the related parameter vertex-neighbor-integrity.","PeriodicalId":53990,"journal":{"name":"JOURNAL OF INTERCONNECTION NETWORKS","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-09-26","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/s0219265923500196","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
The integrity of a graph [Formula: see text] is defined as the minimum value of [Formula: see text] taken over all [Formula: see text], where [Formula: see text] denotes the maximum cardinality of a component of graph [Formula: see text]. In this paper, we investigate bounds on the maximum and minimum values of the weighted version of this parameter. We also consider the same question for the related parameter vertex-neighbor-integrity.
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.
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