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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2017-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1348-5 |
| Summary: | 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. |
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| ISSN: | 1029-242X |