Mixed metric dimension and exchange property of hexagonal nano-network
Abstract The mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount. In this article, we calculate the mixed metric dimension of hexagonal nano-network, a modal with significant applicat...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-11-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-77697-9 |
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| author | Peide Liu Sikander Ali Muhammad Azeem Muhammad Kamran Jamil Manzoor Ahmad Zahid Waleed Ali Bandar Almohsen |
| author_facet | Peide Liu Sikander Ali Muhammad Azeem Muhammad Kamran Jamil Manzoor Ahmad Zahid Waleed Ali Bandar Almohsen |
| author_sort | Peide Liu |
| collection | DOAJ |
| description | Abstract The mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount. In this article, we calculate the mixed metric dimension of hexagonal nano-network, a modal with significant applications in nanotechnology and material science. Through rigorous analysis, we set up that the mixed metric dimension of the hexagonal nano-network is exactly three, highlighting its minimal but enough resolving set that uniquely identifies all vertices. Furthermore, we check out the exchange property within this context, demonstrating the robust adaptability of the hexagonal network’s resolving sets. Our findings display that the alternate assets aren’t the handiest preserved but stronger in these nano-networks, allowing for flexible adjustments in resolving sets without compromising the network’s integrity. This examination offers critical insights into the fundamental properties of hexagonal nano-networks, offering a theoretical foundation for future research in nanomaterial design and optimization. The results underscore the potential of leveraging mixed metric dimensions and exchange properties to achieve efficient and scalable solutions in nano-network applications. |
| format | Article |
| id | doaj-art-582bc927432e40de9aab9b1fe7cc1e0a |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-582bc927432e40de9aab9b1fe7cc1e0a2024-11-10T12:23:12ZengNature PortfolioScientific Reports2045-23222024-11-0114111110.1038/s41598-024-77697-9Mixed metric dimension and exchange property of hexagonal nano-networkPeide Liu0Sikander Ali1Muhammad Azeem2Muhammad Kamran Jamil3Manzoor Ahmad Zahid4Waleed Ali5Bandar Almohsen6School of Business Administration, Shandong Women’s UniversityDepartment of Mathematics, Riphah International University LahoreDepartment of Mathematics, Riphah International University LahoreDepartment of Mathematics, Riphah International University LahoreDepartment of Mathematics, COMSATS University IslamabadDepartment of Mathematics, COMSATS University IslamabadDepartment of Mathematics, College of Science, King Saud UniversityAbstract The mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount. In this article, we calculate the mixed metric dimension of hexagonal nano-network, a modal with significant applications in nanotechnology and material science. Through rigorous analysis, we set up that the mixed metric dimension of the hexagonal nano-network is exactly three, highlighting its minimal but enough resolving set that uniquely identifies all vertices. Furthermore, we check out the exchange property within this context, demonstrating the robust adaptability of the hexagonal network’s resolving sets. Our findings display that the alternate assets aren’t the handiest preserved but stronger in these nano-networks, allowing for flexible adjustments in resolving sets without compromising the network’s integrity. This examination offers critical insights into the fundamental properties of hexagonal nano-networks, offering a theoretical foundation for future research in nanomaterial design and optimization. The results underscore the potential of leveraging mixed metric dimensions and exchange properties to achieve efficient and scalable solutions in nano-network applications.https://doi.org/10.1038/s41598-024-77697-9Resolving setMixed resolving setMixed metric dimensionExchange propertyHexagonal network |
| spellingShingle | Peide Liu Sikander Ali Muhammad Azeem Muhammad Kamran Jamil Manzoor Ahmad Zahid Waleed Ali Bandar Almohsen Mixed metric dimension and exchange property of hexagonal nano-network Scientific Reports Resolving set Mixed resolving set Mixed metric dimension Exchange property Hexagonal network |
| title | Mixed metric dimension and exchange property of hexagonal nano-network |
| title_full | Mixed metric dimension and exchange property of hexagonal nano-network |
| title_fullStr | Mixed metric dimension and exchange property of hexagonal nano-network |
| title_full_unstemmed | Mixed metric dimension and exchange property of hexagonal nano-network |
| title_short | Mixed metric dimension and exchange property of hexagonal nano-network |
| title_sort | mixed metric dimension and exchange property of hexagonal nano network |
| topic | Resolving set Mixed resolving set Mixed metric dimension Exchange property Hexagonal network |
| url | https://doi.org/10.1038/s41598-024-77697-9 |
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