Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison
Graph theory serves as a valuable tool across numerous scientific disciplines, offering the means to model and analyze intricate networks. In this study, we explore the application of distance-based topological indices to a variety of graphs, including the total graph of paths, cycles, complete grap...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/4423113 |
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| _version_ | 1846143150911913984 |
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| author | Haseeb Ahmad Muhammad Kamran Siddiqui Muhammad Farhan Hanif Brima Gegbe |
| author_facet | Haseeb Ahmad Muhammad Kamran Siddiqui Muhammad Farhan Hanif Brima Gegbe |
| author_sort | Haseeb Ahmad |
| collection | DOAJ |
| description | Graph theory serves as a valuable tool across numerous scientific disciplines, offering the means to model and analyze intricate networks. In this study, we explore the application of distance-based topological indices to a variety of graphs, including the total graph of paths, cycles, complete graphs, wheel graphs, helm graphs, and the Cartesian product of K1 and Kn. We investigate five distance-based indices: the Wiener index, multiplicative Wiener index, hyper-Wiener index, Harary index, and average distance. Through detailed analysis, we derive general formulas for these indices and test them on the specified graphs. Using MATLAB for numerical comparisons, we demonstrate the effectiveness of these indices in capturing the structural properties of different graph types. The findings from this study enhance our understanding of topological indices and their applications within the field of graph theory. |
| format | Article |
| id | doaj-art-96bd6783b6e84adfb218892d3eb5fa8e |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-96bd6783b6e84adfb218892d3eb5fa8e2024-12-03T00:00:09ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/jom/4423113Exploring the Distance-Based Topological Indices for Total Graphs via Numerical ComparisonHaseeb Ahmad0Muhammad Kamran Siddiqui1Muhammad Farhan Hanif2Brima Gegbe3Department of MathematicsDepartment of MathematicsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsGraph theory serves as a valuable tool across numerous scientific disciplines, offering the means to model and analyze intricate networks. In this study, we explore the application of distance-based topological indices to a variety of graphs, including the total graph of paths, cycles, complete graphs, wheel graphs, helm graphs, and the Cartesian product of K1 and Kn. We investigate five distance-based indices: the Wiener index, multiplicative Wiener index, hyper-Wiener index, Harary index, and average distance. Through detailed analysis, we derive general formulas for these indices and test them on the specified graphs. Using MATLAB for numerical comparisons, we demonstrate the effectiveness of these indices in capturing the structural properties of different graph types. The findings from this study enhance our understanding of topological indices and their applications within the field of graph theory.http://dx.doi.org/10.1155/jom/4423113 |
| spellingShingle | Haseeb Ahmad Muhammad Kamran Siddiqui Muhammad Farhan Hanif Brima Gegbe Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison Journal of Mathematics |
| title | Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison |
| title_full | Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison |
| title_fullStr | Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison |
| title_full_unstemmed | Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison |
| title_short | Exploring the Distance-Based Topological Indices for Total Graphs via Numerical Comparison |
| title_sort | exploring the distance based topological indices for total graphs via numerical comparison |
| url | http://dx.doi.org/10.1155/jom/4423113 |
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