On the Laplacian spectral radii of Halin graphs
Abstract Let T be a tree with at least four vertices, none of which has degree 2, embedded in the plane. A Halin graph is a plane graph constructed by connecting the leaves of T into a cycle. Thus the cycle C forms the outer face of the Halin graph, with the tree inside it. Let G be a Halin graph wi...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-04-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1348-5 |
| _version_ | 1818416549497667584 |
|---|---|
| author | Huicai Jia Jie Xue |
| author_facet | Huicai Jia Jie Xue |
| author_sort | Huicai Jia |
| collection | DOAJ |
| description | Abstract Let T be a tree with at least four vertices, none of which has degree 2, embedded in the plane. A Halin graph is a plane graph constructed by connecting the leaves of T into a cycle. Thus the cycle C forms the outer face of the Halin graph, with the tree inside it. Let G be a Halin graph with order n. Denote by μ ( G ) $\mu(G)$ the Laplacian spectral radius of G. This paper determines all the Halin graphs with μ ( G ) ≥ n − 4 $\mu(G)\geq n-4$ . Moreover, we obtain the graphs with the first three largest Laplacian spectral radius among all the Halin graphs on n vertices. |
| first_indexed | 2024-12-14T11:52:39Z |
| format | Article |
| id | doaj.art-420f9a9decaa4a929b96c6bc2754e361 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-14T11:52:39Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-420f9a9decaa4a929b96c6bc2754e3612022-12-21T23:02:14ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-04-012017111810.1186/s13660-017-1348-5On the Laplacian spectral radii of Halin graphsHuicai Jia0Jie Xue1Department of Mathematics, School of Information, Renmin University of ChinaDepartment of Computer Science and Technology, East China Normal UniversityAbstract Let T be a tree with at least four vertices, none of which has degree 2, embedded in the plane. A Halin graph is a plane graph constructed by connecting the leaves of T into a cycle. Thus the cycle C forms the outer face of the Halin graph, with the tree inside it. Let G be a Halin graph with order n. Denote by μ ( G ) $\mu(G)$ the Laplacian spectral radius of G. This paper determines all the Halin graphs with μ ( G ) ≥ n − 4 $\mu(G)\geq n-4$ . Moreover, we obtain the graphs with the first three largest Laplacian spectral radius among all the Halin graphs on n vertices.http://link.springer.com/article/10.1186/s13660-017-1348-5Halin graphsLaplacian spectral radius |
| spellingShingle | Huicai Jia Jie Xue On the Laplacian spectral radii of Halin graphs Journal of Inequalities and Applications Halin graphs Laplacian spectral radius |
| title | On the Laplacian spectral radii of Halin graphs |
| title_full | On the Laplacian spectral radii of Halin graphs |
| title_fullStr | On the Laplacian spectral radii of Halin graphs |
| title_full_unstemmed | On the Laplacian spectral radii of Halin graphs |
| title_short | On the Laplacian spectral radii of Halin graphs |
| title_sort | on the laplacian spectral radii of halin graphs |
| topic | Halin graphs Laplacian spectral radius |
| url | http://link.springer.com/article/10.1186/s13660-017-1348-5 |
| work_keys_str_mv | AT huicaijia onthelaplacianspectralradiiofhalingraphs AT jiexue onthelaplacianspectralradiiofhalingraphs |