A novel algebraic technique for adjacency matrices of some derived graphs
Graph energy has been the main concern of spectral graph theory in the last five decades. The classical graph energy is the sum of the absolute values of the eigenvalues of the adjacency matrix. In many research papers, different versions of graph energy by utilizing different graph matrices are int...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Mathematical and Computer Modelling of Dynamical Systems |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/13873954.2025.2535726 |
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| author | Hacer Ozden Ayna Aysun Yurttas Gunes Sadik Delen Medha Itagi Huilgol Berke Ozmen Ismail Naci Cangul |
| author_facet | Hacer Ozden Ayna Aysun Yurttas Gunes Sadik Delen Medha Itagi Huilgol Berke Ozmen Ismail Naci Cangul |
| author_sort | Hacer Ozden Ayna |
| collection | DOAJ |
| description | Graph energy has been the main concern of spectral graph theory in the last five decades. The classical graph energy is the sum of the absolute values of the eigenvalues of the adjacency matrix. In many research papers, different versions of graph energy by utilizing different graph matrices are introduced. For many graph types corresponding to molecular structures, the energy is determined. The theory is complete for complete bipartite graphs. For derived graphs, the problem was settled partially for line, total, double and subdivision graphs. In this paper, the more complex cases of power graphs, shadow, image and core graphs are discussed, and the adjacency matrices of these derived graph classes are formed in terms of very simple submatrices. |
| format | Article |
| id | doaj-art-104ae4bec4ca47eab80d0c33048d2a34 |
| institution | Kabale University |
| issn | 1387-3954 1744-5051 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Mathematical and Computer Modelling of Dynamical Systems |
| spelling | doaj-art-104ae4bec4ca47eab80d0c33048d2a342025-08-20T03:34:10ZengTaylor & Francis GroupMathematical and Computer Modelling of Dynamical Systems1387-39541744-50512025-12-0131110.1080/13873954.2025.2535726A novel algebraic technique for adjacency matrices of some derived graphsHacer Ozden Ayna0Aysun Yurttas Gunes1Sadik Delen2Medha Itagi Huilgol3Berke Ozmen4Ismail Naci Cangul5Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Bursa, TurkeyDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Bursa, TurkeyDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Bursa, TurkeyDepartment of Mathematics, Bangalore University, Bengaluru, IndiaDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Bursa, TurkeyDepartment of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Bursa, TurkeyGraph energy has been the main concern of spectral graph theory in the last five decades. The classical graph energy is the sum of the absolute values of the eigenvalues of the adjacency matrix. In many research papers, different versions of graph energy by utilizing different graph matrices are introduced. For many graph types corresponding to molecular structures, the energy is determined. The theory is complete for complete bipartite graphs. For derived graphs, the problem was settled partially for line, total, double and subdivision graphs. In this paper, the more complex cases of power graphs, shadow, image and core graphs are discussed, and the adjacency matrices of these derived graph classes are formed in terms of very simple submatrices.https://www.tandfonline.com/doi/10.1080/13873954.2025.2535726Adjacency matrixderived graphline graph05C07, 05C10, 05C30, 68R10 |
| spellingShingle | Hacer Ozden Ayna Aysun Yurttas Gunes Sadik Delen Medha Itagi Huilgol Berke Ozmen Ismail Naci Cangul A novel algebraic technique for adjacency matrices of some derived graphs Mathematical and Computer Modelling of Dynamical Systems Adjacency matrix derived graph line graph 05C07, 05C10, 05C30, 68R10 |
| title | A novel algebraic technique for adjacency matrices of some derived graphs |
| title_full | A novel algebraic technique for adjacency matrices of some derived graphs |
| title_fullStr | A novel algebraic technique for adjacency matrices of some derived graphs |
| title_full_unstemmed | A novel algebraic technique for adjacency matrices of some derived graphs |
| title_short | A novel algebraic technique for adjacency matrices of some derived graphs |
| title_sort | novel algebraic technique for adjacency matrices of some derived graphs |
| topic | Adjacency matrix derived graph line graph 05C07, 05C10, 05C30, 68R10 |
| url | https://www.tandfonline.com/doi/10.1080/13873954.2025.2535726 |
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