Mohammed Alsharafi, Abdu Alameri, Yusuf Zeren, Mahioub Shubatah, Anwar Alwardi
{"title":"The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus","authors":"Mohammed Alsharafi, Abdu Alameri, Yusuf Zeren, Mahioub Shubatah, Anwar Alwardi","doi":"10.1155/2024/4269325","DOIUrl":null,"url":null,"abstract":"Topological descriptors play a significant role in chemical nanostructures. These topological measures have explicit chemical uses in chemistry, medicine, biology, and computer sciences. This study calculates the <i>Y</i>-index of some graphs and complements graph operations such as join, tensor and Cartesian and strong products, composition, disjunction, and symmetric difference between two simple graphs. Moreover, the <i>Y</i>-polynomial of titania nanotubes and the formulae for the <i>Y</i>-index, <i>Y</i>-polynomial, <i>F</i>-index, <i>F</i>-polynomial, and <i>Y</i>-coindex of the <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 59.544 12.7178\" width=\"59.544pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.475,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,18.529,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,27.174,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.121,0)\"><use xlink:href=\"#g121-65\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,40.766,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,45.712,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,50.197,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,56.58,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"61.674183799999994 -9.28833 12.455 12.7178\" width=\"12.455pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,61.724,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,69.434,0)\"></path></g></svg></span> and <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 73.136 12.7178\" width=\"73.136pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g190-73\"></use></g><g transform=\"matrix(.013,0,0,-0.013,9.475,0)\"><use xlink:href=\"#g190-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,18.529,0)\"><use xlink:href=\"#g121-65\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,27.174,3.132)\"><use xlink:href=\"#g50-54\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.121,0)\"><use xlink:href=\"#g121-65\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,40.766,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,45.712,0)\"><use xlink:href=\"#g121-65\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,54.357,3.132)\"><use xlink:href=\"#g50-56\"></use></g><g transform=\"matrix(.013,0,0,-0.013,59.304,0)\"><use xlink:href=\"#g113-92\"></use></g><g transform=\"matrix(.013,0,0,-0.013,63.789,0)\"><use xlink:href=\"#g113-114\"></use></g><g transform=\"matrix(.013,0,0,-0.013,70.172,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"75.2651838 -9.28833 12.488 12.7178\" width=\"12.488pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,75.315,0)\"><use xlink:href=\"#g113-113\"></use></g><g transform=\"matrix(.013,0,0,-0.013,83.025,0)\"><use xlink:href=\"#g113-94\"></use></g></svg></span> nanotubes and their molecular complement graphs have been investigated.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"11 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/4269325","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Topological descriptors play a significant role in chemical nanostructures. These topological measures have explicit chemical uses in chemistry, medicine, biology, and computer sciences. This study calculates the Y-index of some graphs and complements graph operations such as join, tensor and Cartesian and strong products, composition, disjunction, and symmetric difference between two simple graphs. Moreover, the Y-polynomial of titania nanotubes and the formulae for the Y-index, Y-polynomial, F-index, F-polynomial, and Y-coindex of the and nanotubes and their molecular complement graphs have been investigated.
期刊介绍：
Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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