{"title":"纳米结构 TUC4C8 和 GTUC 邻域不规则拓扑指数的数学概念和实证研究","authors":"Shahid Zaman, Asad Ullah, Rabia Naseer, Kavi Bahri Rasool","doi":"10.1155/2024/7521699","DOIUrl":null,"url":null,"abstract":"A topological index is a structural descriptor of any molecule/nanostructure that characterizes its topology. In the QSAR and QSPR research, topological indices are employed to predict the physical characteristics associated with bioactivities and chemical reactivity within specific networks. 2D nanostructured materials have many exhibit numerous chemical, mechanical, and physical features. These nanomaterials are exceptionally thin, displaying high chemical functionality and anisotropy. For applications necessitating robust surface interactions on a small scale, 2D materials stand out as the optimal choice due to their expansive surface area and status as the thinnest among all discovered materials. This paper characterized the neighborhood irregular topological invariants of nanostructures <svg height=\"8.98583pt\" style=\"vertical-align:-0.2324905pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.75334 26.432 8.98583\" width=\"26.432pt\" 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,-0.013,8.021,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,17.589,0)\"></path></g></svg><sub>4</sub><svg height=\"9.01194pt\" style=\"vertical-align:-0.2455397pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.7664 8.77705 9.01194\" width=\"8.77705pt\" 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></svg><sub>8</sub>[<i>p</i>, <svg height=\"9.39034pt\" style=\"vertical-align:-3.42943pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 6.50656 9.39034\" width=\"6.50656pt\" 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=\"#g113-114\"></use></g></svg>] and GTUC[<i>p</i>, <i>q</i>] and derived closed form expressions for them. A comparative analysis is then performed on the basis of these computed indices.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical Concepts and Empirical Study of Neighborhood Irregular Topological Indices of Nanostructures TUC4C8 and GTUC\",\"authors\":\"Shahid Zaman, Asad Ullah, Rabia Naseer, Kavi Bahri Rasool\",\"doi\":\"10.1155/2024/7521699\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A topological index is a structural descriptor of any molecule/nanostructure that characterizes its topology. In the QSAR and QSPR research, topological indices are employed to predict the physical characteristics associated with bioactivities and chemical reactivity within specific networks. 2D nanostructured materials have many exhibit numerous chemical, mechanical, and physical features. These nanomaterials are exceptionally thin, displaying high chemical functionality and anisotropy. For applications necessitating robust surface interactions on a small scale, 2D materials stand out as the optimal choice due to their expansive surface area and status as the thinnest among all discovered materials. This paper characterized the neighborhood irregular topological invariants of nanostructures <svg height=\\\"8.98583pt\\\" style=\\\"vertical-align:-0.2324905pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.75334 26.432 8.98583\\\" width=\\\"26.432pt\\\" 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,-0.013,8.021,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,17.589,0)\\\"></path></g></svg><sub>4</sub><svg height=\\\"9.01194pt\\\" style=\\\"vertical-align:-0.2455397pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.7664 8.77705 9.01194\\\" width=\\\"8.77705pt\\\" 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></svg><sub>8</sub>[<i>p</i>, <svg height=\\\"9.39034pt\\\" style=\\\"vertical-align:-3.42943pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -5.96091 6.50656 9.39034\\\" width=\\\"6.50656pt\\\" 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=\\\"#g113-114\\\"></use></g></svg>] and GTUC[<i>p</i>, <i>q</i>] and derived closed form expressions for them. 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Mathematical Concepts and Empirical Study of Neighborhood Irregular Topological Indices of Nanostructures TUC4C8 and GTUC
A topological index is a structural descriptor of any molecule/nanostructure that characterizes its topology. In the QSAR and QSPR research, topological indices are employed to predict the physical characteristics associated with bioactivities and chemical reactivity within specific networks. 2D nanostructured materials have many exhibit numerous chemical, mechanical, and physical features. These nanomaterials are exceptionally thin, displaying high chemical functionality and anisotropy. For applications necessitating robust surface interactions on a small scale, 2D materials stand out as the optimal choice due to their expansive surface area and status as the thinnest among all discovered materials. This paper characterized the neighborhood irregular topological invariants of nanostructures 48[p, ] and GTUC[p, q] and derived closed form expressions for them. A comparative analysis is then performed on the basis of these computed indices.
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.