{"title":"Unraveling the enigmatic irregular coloring of Honeycomb Networks","authors":"","doi":"10.1016/j.dam.2024.09.013","DOIUrl":null,"url":null,"abstract":"<div><div>The honeycomb mesh, based on the hexagonal tessellation, is considered a multiprocessor interconnection network. Cellular phone station placement, computer graphics and image processing are some applications where hexagonal tessellations are used. They are also used for the representation of benzenoid hydrocarbons. In this paper, we study the irregular chromatic number of Honeycomb Network, Honeycomb Cup Network and Honeycomb Torus and establish an exact value for the same. Also, we find an upper bound for the Honeycomb Rhombic and Rectangular Torus networks.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24004037","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The honeycomb mesh, based on the hexagonal tessellation, is considered a multiprocessor interconnection network. Cellular phone station placement, computer graphics and image processing are some applications where hexagonal tessellations are used. They are also used for the representation of benzenoid hydrocarbons. In this paper, we study the irregular chromatic number of Honeycomb Network, Honeycomb Cup Network and Honeycomb Torus and establish an exact value for the same. Also, we find an upper bound for the Honeycomb Rhombic and Rectangular Torus networks.
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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