A Study on Minimal Doubly Resolving Sets of Certain Families of Networks
The suppression of harmful information and even its diffusion can be predicted and delayed by precisely finding sources with limited resources. The doubly resolving sets (DRSs) play a crucial role in determining where diffusion occurs in a network. Source detection problems are among the most challe...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10143649/ |
| _version_ | 1797804889595707392 |
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| author | Muhammad Ahmad Zohaib Zahid Muhammad Javaid Mamo Abebe Ashebo |
| author_facet | Muhammad Ahmad Zohaib Zahid Muhammad Javaid Mamo Abebe Ashebo |
| author_sort | Muhammad Ahmad |
| collection | DOAJ |
| description | The suppression of harmful information and even its diffusion can be predicted and delayed by precisely finding sources with limited resources. The doubly resolving sets (DRSs) play a crucial role in determining where diffusion occurs in a network. Source detection problems are among the most challenging and exciting problems in complex networks. This problem has great significance in controlling any diffusion outbreak. The detection of a virus source in a network is basically locating a node that spreads the observed diffusion. This problem can be solved by using its connection to the well-known and well-studied minimal doubly resolving set (MDRS) problem, which reduces the number of observers needed to get an accurate answer. In this article, we investigate the MDRSs for the families of kayak paddle networks <inline-formula> <tex-math notation="LaTeX">$KP_{(r, s, t)}$ </tex-math></inline-formula> and lollipop networks <inline-formula> <tex-math notation="LaTeX">$L_{(r,s)}$ </tex-math></inline-formula>. It is concluded that the cardinality of MDRSs for <inline-formula> <tex-math notation="LaTeX">$KP_{(r, s, t)}$ </tex-math></inline-formula> is bounded, and it is unbounded for <inline-formula> <tex-math notation="LaTeX">$L_{(r,s)}$ </tex-math></inline-formula>. |
| first_indexed | 2024-03-13T05:42:44Z |
| format | Article |
| id | doaj.art-7c024550ab684078a37b6009b309ef3f |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-13T05:42:44Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-7c024550ab684078a37b6009b309ef3f2023-06-13T23:00:37ZengIEEEIEEE Access2169-35362023-01-0111563445635210.1109/ACCESS.2023.328270110143649A Study on Minimal Doubly Resolving Sets of Certain Families of NetworksMuhammad Ahmad0https://orcid.org/0000-0002-8989-2847Zohaib Zahid1Muhammad Javaid2Mamo Abebe Ashebo3https://orcid.org/0000-0001-8096-0893Department of Mathematics, School of Science, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, School of Science, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, Wollega University, Nekemte, EthiopiaThe suppression of harmful information and even its diffusion can be predicted and delayed by precisely finding sources with limited resources. The doubly resolving sets (DRSs) play a crucial role in determining where diffusion occurs in a network. Source detection problems are among the most challenging and exciting problems in complex networks. This problem has great significance in controlling any diffusion outbreak. The detection of a virus source in a network is basically locating a node that spreads the observed diffusion. This problem can be solved by using its connection to the well-known and well-studied minimal doubly resolving set (MDRS) problem, which reduces the number of observers needed to get an accurate answer. In this article, we investigate the MDRSs for the families of kayak paddle networks <inline-formula> <tex-math notation="LaTeX">$KP_{(r, s, t)}$ </tex-math></inline-formula> and lollipop networks <inline-formula> <tex-math notation="LaTeX">$L_{(r,s)}$ </tex-math></inline-formula>. It is concluded that the cardinality of MDRSs for <inline-formula> <tex-math notation="LaTeX">$KP_{(r, s, t)}$ </tex-math></inline-formula> is bounded, and it is unbounded for <inline-formula> <tex-math notation="LaTeX">$L_{(r,s)}$ </tex-math></inline-formula>.https://ieeexplore.ieee.org/document/10143649/Kayak paddle graphslollipop graphsresolving and doubly resolving setsmetric dimensiondouble metric dimension |
| spellingShingle | Muhammad Ahmad Zohaib Zahid Muhammad Javaid Mamo Abebe Ashebo A Study on Minimal Doubly Resolving Sets of Certain Families of Networks IEEE Access Kayak paddle graphs lollipop graphs resolving and doubly resolving sets metric dimension double metric dimension |
| title | A Study on Minimal Doubly Resolving Sets of Certain Families of Networks |
| title_full | A Study on Minimal Doubly Resolving Sets of Certain Families of Networks |
| title_fullStr | A Study on Minimal Doubly Resolving Sets of Certain Families of Networks |
| title_full_unstemmed | A Study on Minimal Doubly Resolving Sets of Certain Families of Networks |
| title_short | A Study on Minimal Doubly Resolving Sets of Certain Families of Networks |
| title_sort | study on minimal doubly resolving sets of certain families of networks |
| topic | Kayak paddle graphs lollipop graphs resolving and doubly resolving sets metric dimension double metric dimension |
| url | https://ieeexplore.ieee.org/document/10143649/ |
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