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...
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Springer
2017-04-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1348-5 |
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doaj-art-420f9a9decaa4a929b96c6bc2754e3612018-08-15T21:04:02ZengSpringerJournal 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 |
| institution |
Open Data Bank |
| collection |
Open Access Journals |
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Directory of Open Access Journals |
| language |
English |
| format |
Article |
| author |
Huicai Jia Jie Xue |
| spellingShingle |
Huicai Jia Jie Xue On the Laplacian spectral radii of Halin graphs Journal of Inequalities and Applications Halin graphs Laplacian spectral radius |
| author_facet |
Huicai Jia Jie Xue |
| author_sort |
Huicai Jia |
| title |
On the Laplacian spectral radii of Halin graphs |
| title_short |
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_sort |
on the laplacian spectral radii of halin graphs |
| publisher |
Springer |
| series |
Journal of Inequalities and Applications |
| issn |
1029-242X |
| publishDate |
2017-04-01 |
| 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. |
| topic |
Halin graphs Laplacian spectral radius |
| url |
http://link.springer.com/article/10.1186/s13660-017-1348-5 |
| _version_ |
1612707028619231232 |