The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks
Let Hn be the linear heptagonal networks with 2n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of Hn, we utilize the method of decompositions. Thus, the Laplacian spectrum of Hn is created by eigenvalues of a...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/5584167 |
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| author | Jia-Bao Liu Jing Chen Jing Zhao Shaohui Wang |
| author_facet | Jia-Bao Liu Jing Chen Jing Zhao Shaohui Wang |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | Let Hn be the linear heptagonal networks with 2n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of Hn, we utilize the method of decompositions. Thus, the Laplacian spectrum of Hn is created by eigenvalues of a pair of matrices: LA and LS of order numbers 5n+1 and 4n+1n!/r!n−r!, respectively. On the basis of the roots and coefficients of their characteristic polynomials of LA and LS, we get not only the explicit forms of Kirchhoff index but also the corresponding total number of spanning trees of Hn. |
| format | Article |
| id | doaj-art-11b8da2a09ee4a70baafab3f31fbd5be |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-11b8da2a09ee4a70baafab3f31fbd5be2025-08-20T03:54:11ZengWileyComplexity1099-05262022-01-01202210.1155/2022/5584167The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal NetworksJia-Bao Liu0Jing Chen1Jing Zhao2Shaohui Wang3School of Mathematics and PhysicsSchool of Mathematics and PhysicsSchool of Mathematics and PhysicsDepartment of MathematicsLet Hn be the linear heptagonal networks with 2n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of Hn, we utilize the method of decompositions. Thus, the Laplacian spectrum of Hn is created by eigenvalues of a pair of matrices: LA and LS of order numbers 5n+1 and 4n+1n!/r!n−r!, respectively. On the basis of the roots and coefficients of their characteristic polynomials of LA and LS, we get not only the explicit forms of Kirchhoff index but also the corresponding total number of spanning trees of Hn.http://dx.doi.org/10.1155/2022/5584167 |
| spellingShingle | Jia-Bao Liu Jing Chen Jing Zhao Shaohui Wang The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks Complexity |
| title | The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks |
| title_full | The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks |
| title_fullStr | The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks |
| title_full_unstemmed | The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks |
| title_short | The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks |
| title_sort | laplacian spectrum kirchhoff index and the number of spanning trees of the linear heptagonal networks |
| url | http://dx.doi.org/10.1155/2022/5584167 |
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