The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networks
This paper introduces a novel graph invariant, the symmetric division Szeged index (SDZ), which generalizes earlier concepts by focusing on vertices positioned closer to an edge's endpoints rather than vertex degrees. It explores several properties and inequalities associated with the SDZ-index...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844025006607 |
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| author | Modjtaba Ghorbani Zahra Vaziri Razie Alidehi-Ravandi Yilun Shang |
| author_facet | Modjtaba Ghorbani Zahra Vaziri Razie Alidehi-Ravandi Yilun Shang |
| author_sort | Modjtaba Ghorbani |
| collection | DOAJ |
| description | This paper introduces a novel graph invariant, the symmetric division Szeged index (SDZ), which generalizes earlier concepts by focusing on vertices positioned closer to an edge's endpoints rather than vertex degrees. It explores several properties and inequalities associated with the SDZ-index, offering examples and results for various graph classes, including bipartite graphs, trees, complete graphs, unicycles, distance-balanced graphs, and triangle-free graphs. Additionally, the SDZ-index is contrasted with other well-known graph indices. The behavior of the SDZ-index under graph operations, such as corona, sum, lexicographic, and Cartesian products, is also examined. The study highlights the index's potential in topological analysis, particularly in revealing statistically significant correlations with the molecular properties of octane isomers. As research progresses, we anticipate further developments and applications that will enhance our comprehension of complex systems and their properties across fields like network science, computer science, and physics. |
| format | Article |
| id | doaj-art-877513e4e7444602a3e93e8fbd4519c1 |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-877513e4e7444602a3e93e8fbd4519c12025-02-06T05:12:35ZengElsevierHeliyon2405-84402025-02-01113e42280The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networksModjtaba Ghorbani0Zahra Vaziri1Razie Alidehi-Ravandi2Yilun Shang3Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, Iran; Corresponding author.Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, IranDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, IranDepartment of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne, NE1 8ST, UKThis paper introduces a novel graph invariant, the symmetric division Szeged index (SDZ), which generalizes earlier concepts by focusing on vertices positioned closer to an edge's endpoints rather than vertex degrees. It explores several properties and inequalities associated with the SDZ-index, offering examples and results for various graph classes, including bipartite graphs, trees, complete graphs, unicycles, distance-balanced graphs, and triangle-free graphs. Additionally, the SDZ-index is contrasted with other well-known graph indices. The behavior of the SDZ-index under graph operations, such as corona, sum, lexicographic, and Cartesian products, is also examined. The study highlights the index's potential in topological analysis, particularly in revealing statistically significant correlations with the molecular properties of octane isomers. As research progresses, we anticipate further developments and applications that will enhance our comprehension of complex systems and their properties across fields like network science, computer science, and physics.http://www.sciencedirect.com/science/article/pii/S2405844025006607Symmetric division Szeged index (SDZ)Vertex degreesGraph operationsChemical graph theory |
| spellingShingle | Modjtaba Ghorbani Zahra Vaziri Razie Alidehi-Ravandi Yilun Shang The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networks Heliyon Symmetric division Szeged index (SDZ) Vertex degrees Graph operations Chemical graph theory |
| title | The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networks |
| title_full | The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networks |
| title_fullStr | The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networks |
| title_full_unstemmed | The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networks |
| title_short | The symmetric division Szeged index: A novel tool for predicting physical and chemical properties of complex networks |
| title_sort | symmetric division szeged index a novel tool for predicting physical and chemical properties of complex networks |
| topic | Symmetric division Szeged index (SDZ) Vertex degrees Graph operations Chemical graph theory |
| url | http://www.sciencedirect.com/science/article/pii/S2405844025006607 |
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