starlike tree
{{Short description|Tree graph with exactly one vertex of degree >2}}
In the area of mathematics known as graph theory, a tree is said to be starlike if it has exactly one vertex of degree greater than 2. This high-degree vertex is the root and a starlike tree is obtained by attaching at least three linear graphs to this central vertex.
Properties
Two finite starlike trees are isospectral, i.e. their graph Laplacians have the same spectra, if and only if they are isomorphic.M. Lepovic, I. Gutman (2001). [https://www.sciencedirect.com/science/article/pii/S0012365X01001698 No starlike trees are cospectral.] The graph Laplacian has always only one eigenvalue equal or greater than 4.{{cite journal | last1=Nakatsukasa | first1=Yuji | last2=Saito | first2=Naoki | last3=Woei | first3=Ernest | title=Mysteries around the Graph Laplacian Eigenvalue 4 | journal=Linear Algebra and Its Applications | volume=438 | issue=8 | pages=3231–46 | date=April 2013 | doi=10.1016/j.laa.2012.12.012 | arxiv=1112.4526}}
References
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External links
- {{MathWorld | title=Spider Graph |id=SpiderGraph}}
- {{OEIS|A004250}}
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